I've been trying to get into League of Legends recently, but I've been having trouble bridging the gap between knowing the mechanics of the game and actually being able to play online. It seems like most of the "Beginner Guides" out there just outline the basics of last-hitting and leveling, but don't really get into strategy or roles of different heroes. More advanced tutorials seem to just get into infodump territory. Basically, I'm just looking for a guide or series of guides that will allow me to get through a game online without seeming like a complete dumbass. What's a good hero for a beginner to be using? What gear should I be buying for that character and in what general order? What is their basic role? How do I effectively go about attacking other heroes or defending against attacks? (AI games are pretty poor with that because the AI never really leaves their lane or goes for ganks or anything). Basically so far I've learned a lot of the mechanics, but no theory on how to actually be effective with it.

Sure, hit the Giant Bomb chat or add Detrian online and we'll 1v1.

Several of your questons are tricky to answer without more informaton. What hero should you learn with, well what role are you most intrested in? If, like me, you're awful with Melee DPS a recommendation of Master Yi is going to do nothing but leave you frustrated and want to quit the game, if you like being in the front lines you'll hate learning the game as Sona etc. etc.
Once you've got a role you like (or 2, a bit of variation is more fun then just doing the same thing over and over) then a cheap good/great Champion to learn with can be found. Some people think the more expensive the better but this isn't true. For example if you like playing Tank you can pick up Amumu for 1350IP and he's arguably the best damn tank in the game.
 
The specifics of an item build and tactics for any given Champion are best taught 1-1 so take up Detrian on his offer. Some general advice though: 
-Don't chase the enemy too long and too hard. I know it's frustrating when you've got the guy down to the point where a single hit will finish him, but if you can't see the rest of their team on the mini map chances are they're hiding in the bushes just ahead, and the guy you're chasing is leading you right into them. This has got me killed more times then I can count (and I know I'm not alone in that), I know it's really annoying but just let it go.
-Ward the river Bushes next to your lane. When you go back for the first time and buy your gear, if you have 75G+ spare pick up a Vision Ward and drop it in the river bushes. The map-awareness it offers that allows you to push in relative safety is worth the money. Noone else will do this at the low-level play you (and I) play at, so don't rely on your teammates to cover warding, you'll have to do it all yourself.
-Some Champions have abilitys to help them escape, Tristana has 2, but some don't. Flash is a good spell on anyone, but on Champs without an escape mechanism it becomes much more important.

PM if you have any questions I'm learning too.

I'm still learning the game myself and it can be overwhelming at times. I've been fortunate enough to have some experienced friends to help me out as well as just reading all of the, as you aptly put it, infodump guides over at places like mobafire. A lot of the guide writers do a terrific job of educating you on the character and even teaching you things like when and where to use wards or how to jungle and such, 
 
I would say try a bunch of the free characters out in vs ai matches or in custom games with friends while having a guide for them open so you can read up on a good item order to build towards as you play. Nothing beats getting actual experience with a character so you can see if you can like how they play, like their abilities, etc.  I'll throw my name out there as someone else you can always PM to ask questions of or if you ever wanna play a match gimme a shout. My name on LoL is the same as my user name here. 
 
Best of luck on learning and enjoying the game. I hated it the first time I played a year ago, but decided to give it another chance and have found champions and roles I really enjoy. :)

You can add Vision and ask anything. :) (US servers)

I am also willing to do some 1v1 time with you.

@PixelPrinny: ZOMG IM GONNA ADD YOU. *STALK STALK*

@Xeiphyer said:

@PixelPrinny: ZOMG IM GONNA ADD YOU. *STALK STALK*

As if I'd let a stalker like you add me! Your Gangplank is so bad when my Janna isn't around. He's all like, "Waa, I run out of mana too fast, I need a mana regen aura so go get Soul Shroud. Waa, I can't slow them down, I need your CC abilites. Waa, I rush in and suicide at level 1 because I'm a bad pirate!"

See also: Basic Concept Guide and The Art of League of Legends (PDF)

I'm still learning the game myself and it can be overwhelming at times. I've been fortunate enough to have some experienced friends to help me out as well as just reading all of the, as you aptly put it, infodump guides over at places like mobafire. A lot of the guide writers do a terrific job of educating you on the character and even teaching you things like when and where to use wards or how to jungle and such,  I would say try a bunch of the free characters out in vs ai matches or in custom games with friends while having a guide for them open so you can read up on a good item order to build towards as you play. Nothing beats getting actual experience with a character so you can see if you can like how they play, like their abilities, etc.  I'll throw my name out there as someone else you can always PM to ask questions of or if you ever wanna play a match gimme a shout. My name on LoL is the same as my user name here.  Best of luck on learning and enjoying the game. I hated it the first time I played a year ago, but decided to give it another chance and have found champions and roles I really enjoy. :)

@Xeiphyer: You said what I was going to word for word :(

@Chadster: But seriously, for learning I would suggest ranged physical damage and using the recommended items until you know the other items well enough to experiment!

Also playing with friends helps a lot, but if you have to go solo don't take anything anyone says to heart and keep practising! :)

don't do it 
it sucks 

LoL!

Oh yeah, I would also recommend NEVER buying tier 2 runes. Too expensive and too little of an upgrade for money that is better spent on a champ you like or saving for tier 3 runes.

No, that game is garbage. Get SC2 and play custom DOTA games on that instead.

I wouldn't recommend a new player start off with a ranged carry like Ashe as you will be spending a large amount of your time dead until you learn positioning and proper pacing of the game. The only way to get good at this game is to play it more and to be alive for more time in the games you will be playing.

The easiest/most durable characters in the game are Garen or Mordekaiser for melee and Gangplank or Fiddlesticks for ranged.

Pushing your lane without dying is the most important part of the game to learn, learning to get kills comes with time and experience.

For gear, just use the recommended, it's almost always a good mix of offensive and defensive items, most guides will completely ignore defensive items which will leave you dead more than you should be when you don't know what you are doing.