Hey, my name is Jam Nuke.
I play on NA and recently I have climbed from Silver V to Gold V, I may have some tips for you.
Here is my LoL king:
http://www.lolking.net/summoner/na/46992682
Focus on yourself.
I know it can be hard if your bot lane is feeding or your jungler isn't ganking, but don't think about them, you can't change the way they play. What you can do is change the way you play. Warding up more and getting more vision that is safe to get, focusing on CS'ing and pinging MIA if your lanes aren't map aware are all example of trying to help your team if they are struggling, if you really do deserve to move up, you can do a lot more to try and carry your team, but, contrary to popular belief, some games just aren't possible to carry, because you and your team weren't playing well enough.
_ People under estimate the power of CS_.
You could be 0/2, but if your laner couldn't snowball of other lanes and failed roams then you would've built up a massive CS lead, and they won't expect that power spike, because lower levels hardly ever look at their laners item builds and if they have snowballed a lead, practice your farming, try and get ahead, if you are a few waves up in CS and they aren't too far ahead in kills, you still are in the game, don't give up.
Practice with someone slightly better than you.
This is an interesting one, play with someone who is slightly better at the game than you, and player normal/ranked, whatever you are comfortable with, you will be matched with other people slightly better than you, this is a very good challenge, this will make it easier for you to figure out what you aren't doing so well at compared to them, maybe you aren't as good at CS'ing, item build is wrong or blindly followed maybe, or just your positioning in lane makes it easy for your opponent to pressure you out of CS, all of these things could be just what is holding you back from high silver. Analyse your games afterwards as well, this will make it even more easy to see where your slip up's are.
Lack of/ Incorrect runes and masteries
These are so important, yet over looked by so many players, the difference between winning or losing your lane early could depend on the runes and masteries that you have, always remember that you can customise mastery pages in champion select, don't bother getting MR if their team is all AD! Customise your rune page to not only suit your champion, but to defend against the enemy.
Getting a full set of generic tier 3 runes are paramount, especially as you get higher ranked. You get 2 rune pages for free, USE THEM, and use them effectively, use a generic page if you lack pages, e.g AD + AS page if you play a lot of ADC.
Widen your champion pool and learn the basics of each role, but stick to what you know in ranked.
Nothing is more awkward when you are last pick and you are left with that role that you just have never played before. Learn the basics of every role and get a feel for all of the play styles and general or common situations you will be in. You don't have to be amazing at each role, just get to know each one.
Have a couple champs that you get to learn and are fairly good at for each role, just in case one is banned out, or is picked by the enemy.
For example for each role I have 3 champs I have established and are comfortable with.
Top:
Gnar
Vladimir
Wukong
JGL:
Master Yi
Elise
Rek'sai
Mid:
Annie
Lux
Katarina
ADC:
Sivir
Kalista
Draven
Support:
Nautlius
Thresh
Annie
So those are just 5 tips that came off the top of my head, good luck ranking up and feel free to add me in game.