LoL has a tutorial mode, where you play just yourself and 4 bots vs 5 bots, and you have your choice of three characters: Garen (a tank), Ryze (an Ability Power mage), and Ashe (an Attack Damage Carry [aka marksman], someone who fights usually at range and does a lot of damage with autoattacks). I'd suggest playing a few games as each to get the feel for each one and decide which style of character you like. The tutorial will walk you through how to play, with reminders to buy items at the start of the game, to try to last hit, and gives visual indicators of the range of turrets so you can more easily make tactical use of them.
Beginnger tips:
--There are three main ways to get gold to buy items: last-hit minions and monsters, kill enemy champions, and destroy enemy turrets. minions will be the main source of gold, so focus on doing that well, because without gold, you will become weaker as the game goes on.
--You get XP whenever you are close to an enemy that dies, even if you didn't attack them. And by close, I mean pretty much if they are on the screen while you have the view zoomed all the way out.
--Turn Smartcasting on for your abilities (and maybe your item slots) and get used to it. It is so much better than without (where you have to hit the ability button, then click you target). Smartcast means when you click an ability, it will use it if your cursor is simply overtop of a valid target for that ability.
--Play with the camera unlocked. Ideally, you want to move the camera manually, but that is a serious pain. The simplest way to play then is to simply hold the spacebar down, which locks the camera while you are holding it. This lets you lock it most of the time, but unlock it simply by letting up, rather than clicking a button on the screen or hitting the Y button.
--Use a site like SoloMid or LoLKing to look up guides on what items to build for the champion you are playing. The difference between a really good build and just a good build is staggering.
--Don't try to take on the Jungler role until your account is level 20 and you have Tier 3 runes for it. Without those, it is just too hard to get a good start with all but a few champions.
As far as champions, there are 5 "roles" in the game: Top, Mid, ADC/Marksman, Support, and Jungler.
Top: Garen is the prototypical Top, as he is a very old champ, can't really pay any other role well, and like most tops, is tanky. renekton is probably the best overall top right now, as he doesn't have much of any bad matchups in lane, though he's weaker late-game than ones like Nasus or Shyvana, and doesn't carry as hard when fed as Fiora or Darius. You'll occasionally see the mobile marksmen like Vayne, Quinn, or Lucian up here as a counterpick to a non-mobile tank like Nasus or Shyvana.
Mid is the lane with the shortest distance between towers, so it is commonly used for the people who have very high burst damage, namely the damage-focused mages and assassins. I find Ryze very hard to work with personally, so I would recommend Annie for a low-cost mage, with Ziggs being a great overall pick due to how safe he can play. On the Assassin, none of them are all that easy to play, but Fizz. Zed, Akali, and Katarina are all solid picks in different ways.
Marksman goes bottom lane typically and focuses on AD damage. Tristana is both inexpensive and the best one right now, with Lucian, Caitlyn, and Jinx all being common picks as well. I'm fond of Miss Fortune's playstyle, personally. This is one role that really has little in the way of good low IP-cost champs.
Support also goes bot-lane to help protect the Marksman. These tend to come in 3 styles, which do have some overlap, but the common theme tends to be good Crowd Control abilities (things that inflict slow, stun, snare, knockup, etc) and not being particularly reliant on gold income to do their job. The tanky supports tend to dive in, disable, and take a beating while their Marksman goes to town, and are most notably Leona, Thresh, and Braum. The more classic Supports focus more on ally heals and buffs with some enemy CC, such as Soraka, Nami, Janna, and Sona. The third type is basically Mid Mages that have good CC and thus can help burst an opponent down while disabling them; see Morgana and Annie as two prime example.
Junglers roam the areas between lanes, farming the monsters there and jumping into lanes from the sides to try to surprise the enemies there for kills. They tend to be very strong at levels 1-3 and have a good form of lifegain built-into their kit. they tend to be at least bruiser-type champs, if not outright tanks, though there are a few assassin-style junglers out there (and just last night, I saw a good Lucian jungle!). Vi, Lee Sin, and Elise are the three top junglers currently, though Master Yi, Warwick, Xin Zhao and Jarvan IV are all pretty common junglers as well.
So i decided i wanted to try LoL and I am currently downloading it. Just wanted to ask for beginner/advanced tips and champions that might be good to start with?