I almost never go positive, my average KDA is like 1/12/8, I've tried every lane and role, and haven't found a main yet. You may say "All new players to League suck" but no, I'm a level 29 (ignore what's next to my name, my accounts are broken and stupid). Still haven't found a main. I fricken fed and lost against intermediate bots. No matter who I choose or play, I just suck all the balls in the worlds (Phreak's especially).
I am just going to be blunt with whats wrong.
So your missing basic rune pages. They have a lot of power for the early game . You have had the ablity to buy teir 3 runes since level 20. you should of had a max out set of runes by this point.
Your playing 3 of the 4 maps (at least on your history you are). You need to settle down on one mode(not ARAM). How each game/map is played is completely different. Your not understanding the basics of any of the modes you are playing.
Jumping around haphazardly from AD to AP is also a problem. Most people by level 10 find a role to work with. You do not seem to have even a role, which only you can figure out. Even generalist players (like me) have preferred roles and started learning a roll at a time.
Your builds are also questionable. VERY QUESTIONABLE.
You will not get better til you deal with these issues. A tip is stay away from ranked. At the rate your playing your going to get very upset and land in bronze 5.
Going along with what Kchaosrei said about just choosing a map and going with it, it might be best to just choose a champ you kind of like to main and run with it.
I chose 
for the dumbest reason ever, but then just decided to focus on her and get good with her by watching Youtube videos of pros and reading a lot of guides that were about her. Doing that I learned a lot more about the game in general than I did in any general guides. I'm still a complete n00b and I'm definitely no Diamond-level Kat player, but I'm a slightly above average n00b, which is better than the feeder that I used to be.
ARAM is your friend.
I had the same problem when I was lvl 29. But it's a bit different from you. I filled 2 basic runes page already when I was lvl 29. I named them Attack Damage and Ability Power. You can check http://www.lolking.net/summoner/na/52220526#profile
I played Co-op vs AI intermediate mode over 100 games to practice my main champ 
untill I had confident to play SR Blind pick mode.
Later on, I played only Normal Draft because it's the same to Ranked Game. I practiced over 200 games with the monkey king before I decided to play Ranked Game in Provisional match. I won 6/10 and jumped to Silver 2. I just wanna share my journey in LOL with you. I learned that Wukong can go to top lane, jungle, and mid. So I practiced with those lanes.
My acc is really simple. You can check it out.
So I started a reply, but it turned into its own post. Hope it can help you!
I don't know about everyone's recommendations to "get a runepage" because really at your level of skill those differences are nice but not gamechangeing. What's going to be most important is learning to farm creeps. You need to pick just a champion or two to work on at first, even if you don't do so well at first, just pick a kit that looks interesting. Don't try the champions that show a higher difficulty. Also remember when playing an ad champ to buy attack damage before attack speed and crit -.- biggest newbie mistake I see.
What KCHAOSREI said is very reasonable and makes good sense to get you started. No need to let the "feeding" get to you. Remember League is a very, VERY hard game and it takes a lot of patience and practice to get good at it (and even when you do there are still times you will feel like an absolute noob).
But yea playing multiple modes is certainly not the way to learn. Decide which map you like and focus only on that (Summoner's Rift is considered the "main" League of Legends but choose whichever you like).
I'd also suggest watching some video guides on YT on how to get better at this game as there are so many things you need to do in a given game that it'll take you a long time to figure them out on your own. There's a channel called Jeremy'sGamingCurios that has a lot of guides on many different aspects of the game. Some may be slightly outdated but the principles are there.
So:
Find your map Find which playstyle you enjoy (which will guide you toward choosing a role) Watch some guides and understand the most important concepts of this game Play. A LOT.
And personally I would suggest against playing a lot ARAM if you want to learn the game, as the playstyle of "one lane, no ganks, 5 man all out" is not present in any other map and doesn't teach you much besides how to dodge skillshots.
Though this may be counterintuitive, but try a FOTM or OP champ. Most of the time, they're relatively easy compared to lower powered champions. Then again, I don't even play ranked, so my opinion is worth little to nothing.
You probably have poor decision making.
I recommend youtube videos or streams or guides if you havent done that yet. There are a ton of skills in a moba game that take a long time to develop.
Runepages
Page 1 Marks: Flat Attack Damage Seals: Flat Armor Glyphs: Flat Magic Resist Quints: Flat Attack Damage.
This page is perfect for normal blinds game and can be used on nearly every role and champion. Even if you want to play a mage mid lane, this runepage will still be a big help to your early game. It wont be as useful later on over something like magic penetration, but rest assured that starting with flat AD is phenomenal on a mage, allowing you to last hit with your auto attacks without much trouble, and giving you that extra poke when you auto attack harass.
Page 2 Marks: Flat Armor Seals: Flat Armor Quints: Gold per 5 Glyphs: Flat Magic resist.
This page is for when you get stuck supporting, or for those champions who would rather have extra armor over early auto attack damage (not many champions). The extra armor in bot lane tho really helps you be a meatshield and tank the enemy ADC without exploding. That extra GP5 is not much but it helps get you that extra gold reach.
These two pages are all you need to get rocking and rolling with just about every position in league of legends. When you get more experience with the game you can start to worry about more focused runpages, like attack speed + armor for a FF jungle for example, or mana for ryze, or possibly even scaling MR glyphs for draft pick options. For now tho, page 1 will be your goto page for most champions, and page 2 will be your goto support page.
Champions.
Top lane
is very strait forward. He is fun to play, can snowball, and only costs 450 IP. Get him for top lane if you havent yet. Read a top lane garen guide thats highly voted. But a quick rundown, Q lvl 1, lvl 2/3 get E, W lvl 4, E lvl 5, R lvl 6. Max E first and Q 2nd, W last. Run runepage 1. Get 9/21/0 masteries, with the butcher passive and the flat attack damage gains per lvl and starting flat attack damage, and the armor / crit reduction in the defensive tree. Build black cleaver first item, and the rest get defensive items. Randiuns and Spirit Visage are great picks. Garen is very straitforward and you cant really fuck up to much. Not much of a difference between a professional garen and bronze league besides last hit mechanics, decision making, and map awareness.
Mid lane
This is the hardest role next to jungle, simply because its the most exposed and open to getting ganked from all angles. I would recommend 
, because she is not that expensive, has great poke and waveclear, and is pretty straitforward. She is immobile and squishy, but if you save your Q hits until you have a shot on the person perusing you, you should be fine. I recommend avoiding this lane because it is the most difficult. If you do play lux, max E first for the poke and Q 2nd, and run 21/0/9 masteries with page 1.
Jungle
This role is difficult because of the burden of knowledge. When to gank and why and when to clear camps and why. I recommend watching youtube videos and streams. But a good faceroll champion for jungle is 
. 21/5/4 masteries (or 21/9/0 whatever) but make sure to pick up the jungle talents in defensive tree. Rush Feral Flare and mobility boots. Max Q first and E 2nd, dont even put a point into W until lvl 13. Master Yi is pretty faceroll because all you have to do is push E, then push Q, and click on enemy. He can carry games and delete everything because he is master Yi.
Support
it doesnt get any more straitforward then this. Okay taric might not be the best champion, but seriously there is not much difference from a bronze taric to a professional besides decision making skills and map awareness.
For ADC take 
. Running out of room for typin
lol @ all the balls in the world
I had a super similar problem to you. I only hit 29 last night, but I used to be completely horrible at the game on a whole. For me, the change came after I watched Worlds. I still play champs they consider unviable, but I've learned how important vision and proper mechanics are.
My recommendation is to find a champion or type of champion you enjoy playing, and start learning them on the lanes they're most useful in.
I've been maining
Top
Jungle
and
if I ever have to ADC.
So what's in common with these champions? You might think it's absolutely nothing, but it's all about their late game damage potential.
Malphite, when built purely AP (Rushing DFG, then Zhonyas), can melt down a tank in under two seconds.
Fiddlesticks has one of the greatest jungle clears of any champion--his E clears small minions, while his Q stops damage from the largest threat, and his W drains you up to full health after any jungle camp. Picking up a blue buff means he can choose to never leave the jungle unless he absolutely must.
Finally, Sivir's an amazing ADC because of her combined ability to launch long range assaults for high damage with her Q, but also because of her ability to waveclear and siege towers while taking down minions waves with her W. SpellShield saves your ass when you see that Lux global ult appear from across the screen, and you get back 90 mana right then and there.
So, it's up to you to figure out where your power goes.
Some of my friends do best with early game power spikers, while others look towards late game (as I do).
So: Good mechanics, comfortable champion play, and smart builds. These are the three things that should help you out.
Guides on Champion Build's / Runes and other general information, just be sure to use the filters for best rated and look for guides with "featured"
Consider this if you need a champion build on the fly, just simply use the search bar and a list of recent builds that pro players used for that specific champion will show up.
You can also watch high level player stream on twitch to help you learn the game.
http://www.twitch.tv/directory/game/League%20of%20Legends
Once you got a good grasp of the game, i would then encourage you to experiment with different builds, masteries and runes to get a stronger understanding of the game as mindlessly following guides / builds from other players can only bring you so far.
Best of Luck!
Movement speed Quints are fine on anyone go ahead with those if you want. I used them for a while when I started and still have them on one of my jungle pages.
As for Irelia. Typical Irelia build is to start with BotrK OR Trinity force and build tankiness after (Randuins is popular). I used to main Irelia in my earlier league days and that build style works on anyone. She likes attack speed for her W. She actually builds a lot like (And is treated such) Jax. She has built in Tenacity so there's no rush (But yes Merc Treads will likely be an eventual buy in your build). But the power spike after finishing BotrK/TriForce is just too strong. You can buy level one boots before you finish it somewhere along the way though.
As for Gauntlet. Trinity force has phage (Which gives you MS when you hit them), Botrk slows. And you have a slow/stun. You'll have plenty of damage after those are finished and Randuin's is pretty strong on Irelia IMO. (Easy to build into, useful passive and active for a "Dive in there" champ)
Like I said, I won't dictate your builds. But those are the items typical Irelias build and the reason they build them.
