How do I build?

I'm currently level 17 and all this time I was just using the recommended items from the shop, when something gets non-greyed, I just double click it and buy it, without bothering to read the description. Lately I've been getting told by some people that building is a really fun aspect of the game and it's what makes the champions feel more personalized and customizeable. I obviously want this, but I just have no clue how to do it. What items do I buy? My main gripe is the fact that all the items are beneficial, so why should I choose one over the other? How do I make a balanced build that doesn't leave one stat(?) in its default value? What do each of the stats(?) mean, like AP, AD, and how on earth do I interpret these ratios, numbers and percentages you guys keep throwing around?!
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