Okay, so all I've been doing when playing league is following the recommended build. I want to start being able to make my own choices when buying my items. The thing is I don't know what to buy, and why I should buy it. Or what makes this item a better choice than another. I'm basically lost without the recommended build. Help?
I think I understand your question. You don't really want people to suggest builds. You want to understand HOW people know to suggest those builds. When I first started league, I had the exact same problem (That was 4 years ago lol).
So, what you can do is go to http://leagueoflegends.wikia.com/wiki/League_of_Legends_Wiki and click on a champion you like. Lets take Volibear for example (Since I play him).
What are you looking for on the Volibear page? Well lets look at his roles first. He's a fighter and a tank. That means he likes tanky stats, but what are tanky stats? Armor, magic resist, and health are tanky stats. They make you harder to kill. If your opponent has a lot of physical damage, get armor. If they have a lot of magic damage, get magic resist. Health mitigates both, but it's more effective if you mix it with some armor or magic resist.
Now, lets look at volibear's abilities. What we are looking for is his "scalings." For example, his passive gets better with more health. W (Frenzy) scales with health. E scales with AP. R scales with AP and attack speed. How do I know R (The ultimate) scales with attack speed? That's because as a rule of thumb, on-hit effects get better with attack speed, and thunder is an on-hit effect. Now you may be thinking "Oh okay, so he has AP ratios. That means I should build AP right?" No not really. Building AP means building damage for those abilities that scale with AP, but Volibear is a tank. You should be prioritizing tanky stats over damage stats. You'll notice that his W damage scales with health. So you can build tanky, and still be gettting some damage out of it.
Also look at the ratios of his two AP abilities. .6 and .3. These scales aren't that good. .6 is okay, but not .3. It wouldn't be worth buying AP items just to boost the damage of these abilities. You job as a tank isn't to do damage. Your job is to be disruptive and survive.
You can apply some of these theories to other champions you find. For example, if you look at Caitlyn you'll notice she is a marksman with lots of AD scalings. That means you want to build AD damage items on her.
I hope this helped a little bit. As you look at other builds, you'll start to understand the reasoning behind certain items. Good guides will explain item choices on the champions they are about. Good luck out there!
Look at the stats of the item and compare them to what your team needs. If your adc is constantly getting caught out, get a 
. Its all about synergy with your champions kit and also the source of damage from the enemy team.
Who/What do you main?
Look at the types of focus the enemy team is building, and who are the most relevant problems. If their carry/majority of the team is AP for example, you would build MR, if it was AD, then Armor. If there are particular abilities/combos/tricks you want to get/counter, then you would build items to help you get around/use them better. And in general, just build to whichever stat would help you with the problems of your own champion (Sustain/CDR/mana/health/damage/etc).
I would say just look up item builds on the 'net. Some items (like Executioner's) are very situational but will help you immensely.
Also read the meta changes it will help you understand items.
I agree with what GuiltyGecko says, but what he left out is that you should also build for the Passives and Actives each item has. For example, let's compare 
Randuin's Omen with 
Dead Man's Plate (I'll be saying them as RO and DMP for ease). RO offers more base stat increases than DMP (+10 Armor and -10 damage from Crit Strikes), but there's a difference between them.
RO's Passive, Cold Steel, reduces your opponent's Attack Speed (AS) by 15% for 1 second; its Active reduces the Movement Speed of nearby opponent units by 35% for 4 seconds. This item is obviously meant to punish and make it easier to deal with opponents who are building Crit percentage (like Yasuo and most Attack Damage Carries (ADCs)).
DMP's first Passive, Dreadnought, builds stacks of Momentum that increases your Movement Speed (MS) by up to 60 at 100 stacks; its second Passive, Crushing Blow, discharges all stacks of Momentum to deal 1 physical damage per 2 stacks and doubles that damage if 100 stacks were discharged. It also inflicts a decaying slow of 50% if the attack was Melee. This item is meant to quickly get your Champion into the action and deal burst damage, while also passively acting as an escape due to Dreadnought.
What I like to do is I like to play a few Co-op vs AI games and test the items out before I use them in PvP, so I know exactly what they do and how I can use them. It's also a good idea to do so if you're not used to using your items' Actives, so you can get used to doing those before you play PvP. Hope our advice is doing well for you :)
champion.gg is a very helpful website, but you also have to buy some things situationally.
are you mid against a leblanc who is shitting on you in lane? probably want 
playing as an adc with an annoying zed? 
team has hard cc and keeps focusing your carries?
tanks too tanky? 
these are just some examples and it takes time to learn items and what they're useful for, but you'll get it with time. the recommended items are definitely a good start but you could also look for resources from other mains of that champion.
personally i prefer /r/summonerschool to learn things, the simple questions post is very helpful if you want to ask something but don't want to be downvoted to hell and called a noob
