For what it's worth, I too go to MOBAfire, and look at builds. I personally don't use them, because I don't like sitting there with a piece of paper going "OK, I got this much gold, I need to get THIS items now" and "OK, I got to THIS level, so now I have to level THIS ability" and so on. I just find it annoying.
I do make my own builds though, and once in a while, if I'm either trying out a new Champ, or trying to think of ideas, I'll go there, and look through the builds, and see what Items they're using, what Masteries they have and why, and of course what Runes they have, and why.
This is a good idea in general because I've personally, on more than one occasion, bought a Champ, started up a practice game (I don't play normal games when I'm doing something for the first time, I don't want my team to suffer if I screw up or it doesn't work) and then start playing, and I realize I don't know what I'm doing.
I have 31 Champs right now, and every one of them I use, the thing I like to do first, is this:
I'll get the Champ, or, if they're free, start up a practice game. Normally I'll do this with a 5v5 game because they last longer, and I have the time to get a better feel for them. I also can get more Gold in the 5v5, so I can try out Items as I go.
Anyway, once I have that going, I'll play, think about the items I'm using and so on, and then, once the game is over, I'll go to MOBAfire, and look at the builds for that Champ. I'll look at the Runes they're using, to see if I liked that particular attribute of that particular Champ, and I'll look at the Items they use, so I can see how they use them, and if I like it.
After a while, I'll end up knowing what I like. For example, I recently bought Jax. I didn't know how to play him very well as I'd only done a few practice games a while back, so I did the same thing as I said; I started up a 5v5 Practice game, looked at, and read ALL of his abilities, to see what I wanted to do first, and then, I saw his Innate, so I knew I wanted some Damage items.
After I had been playing for a while, and had the Gold, I got the Items I felt would work best for him. If I didn't like something, or figured out that something else would possibly work better, I'd sell something else, and then get that item.
After the game, I went on MOBAfire, and started reading how other people played him. I wanted to see not just what Items they used, but how they actually played with him.
I decided that Dodge was a great idea Obviously lol, and so I started getting Dodge Runes. I also ALWAYS get Ninja Tabi with him, and then the Items, I'm still working on it.
I saw that Hextech Gunblade worked REALLY well with Jax, because not only did it do AP, but it also has Damage. So I gain Health Points, and also, the overall stuff that it does, works well. So I wrote that down in a little notebook I have for this, and started thinking about other items and Runes.
I noticed that there was a Mastery that also added Dodge Chance, so I popped the points into that too, and went from there.
I noticed that I personally like Building Jax to do Attack Speed, and Attack Damage. So basically I get Damage Items, Speed Items, and also, something for Mana.
this is something you could try too, because really, every person is different. The way someone plays any Champ, may not be the way YOU want to play them.
You don't have to lose just to play your Champ the way you like to though either. I mean, LoL has a lot of Champs, and a lot of Items. It also has Runes and Masteries that add to that. And Summoner Spells.
I'd personally say that the best advice, would be to look at the Champs you like, play with them until you get a feel for them, and then start thinking about which Items, Runes, Masteries, and so on, will let you do your best with that.
Hope it helps.