The one thing that I think is the most important in MOBAs is simply to learn from playing and from your mistakes. Make a point to play all the free champs and know all the abilities of all the new champs you meet. If you do, you can make better decision on how to play. Are you being stunned by Amumu? Stand behind minions or out of range so his bandage doesn't hit you.
Lasthitting is important, as it ensures you get the gold. Even though 19-26 gold (at the start) per minion doesn't seem much, it adds up. At 15 minutes, there will have spawned 101 minions, which equates to a bit over 2k gold. Even though you personally don't get ALL the lasthits, your lane-mate may get them, and total team gold is nearly as important as personal gold.
Warding is also an important part of the game. It is more important if the other team has a jungler. However, dragon should be warded when it's up, once you reach the 15-20th minute, as that's when most teams without a jungler will take it. Baron (large red skull on the minimap)should be warded after 30-ish minutes. If you can only spare 150 gold, ward dragon and baron.
Dragon gives 190 gold to EVERY member of your team. That's 950 global gold. The 75 gold you spent on that ward can pay off if you can manage to steal dragon. If you lose two people, but get dragon, it is also worth it. It is worth noting that some champions get more out the gold than others. AD carries scale get more damage out of items than, for example, a support champion gets. The roles are:
Ability Power (AP) carry: Usually gets mid, where he will level quicker because he doesn't share experience with anyone. His spells are his main source of damage, therefore more levels will equate to higher levels of spells, and therefore more damage.
Cheap examples: Annie, Veigar, Morgana
Attack Damage (AD) carry: Is typically played in the bottom lane together with a support champion who will allow you all the lasthits, but things will be different at lower levels. These champions are the most dependent on getting last-hits, as they require the most gold to do proper damage. They are typically more dangerous in the late game, as in after 30 minutes, when they have a few items.
Cheap examples: Tristana (free if you like LoL on FB), Ashe.
Support:Not played in every game, and isn't recommended unless you're certain your team will do a good job, as it's hard to ensure the win when you do little damage. Support are generally mostly responsible for warding the key points, which are dragon, baron, and the river bushes at mid, there are more guides for it on the web. If you lane with an AD carry, you can allow the carry to get most of the lasthits, while you build items that grant you gold per 5 seconds. They often gets Clairvoyance.
Cheap examples: Janna, Alistar, Soraka
Assassin:Champions who are squishy, but deal a lot of damage. They can be hard to play, as it can be hard to determine when it is safe to go into combat.
Cheap examples:Master Yi, Shaco, Talon (although he is often built tanky)
Bruiser:[b/]Most often melee champions who can take some punishment. They get some items that offer damage, and some that offer durability. They can get into a teamfight, take out essential targets (carries), and get out again alive. They often get the top lane alone if your team has a jungler.
Cheap examples:Tryndamere, Garen, Cho'Gath
Jungler:A role you will not see that often at lower summoner levels. His role is to level exclusively through killing neutral creeps, and go for kills in lanes, if possible. This gives the team two solo lanes, meaning you will have two champs who level more quickly. A jungler can also be asked to hold your lane if you need to go back to heal or buy. Junglers are also responsible for warding, and for making sure the team takes dragon. Ideally, your jungler, together with the two champions at bottom lane should get dragon at about the 10th minute, and again at the 16th minute.Tanks, who are champions who initiate teamfights, and get all durability items, are typically junglers, as they do not contribute a lot to a lane.
Cheap examplesAmumu, Warwick, Udyr
Jungling should only be done if the top lane can be guarranteed, you need a champion who can take some punishment, and/or has ways of regenerating health. You and your friend can play a jungler/bruiser combo. For example you can play Cho'gath, and he can play Warwick or Amumu. Cho gets hp back from killing minions, and can prevent losing his tower, as long as he has two abilities that push waves back easily. As Cho I would recommend you focus on leveling your W, with a single point in your E for easier lasthitting at some point. Your W is easier to hit than your Q, and it is basically a safer choice.
I usually start with Meki Pendant (Mana regeneration) and two mana potions, or a ward, if the other team has a jungler. Later I build into Fiendish Codex and Morello's Tome. Getting the basic boots somewhat early is quite important, as you will be able to chase champions, or run away from them more easily. Boots+3 hp potions is a decent start if you're playing a melee champion or an AD carry.
Bottom line: I hope you read this, and have some use for it, if not I've wasted quite a lot of time.