League-of-legends – n’t Hecarim trust Mordekaiser

Map Awareness

Riot has garnered some pretty effective videos with their Video Tutorial contest (Links posted below). As a beginner, you want to primarily focus on making sure you don't get ambushed by the other team (called a "gank"). While some of this involves Map Awareness, you also need to learn to not overextend, as well as keeping an eye on the enemies you're fighting in your lane. If you cannot see one or both of the enemies in your lane, let your teammates know!

Last Hitting

Killing minions and enemy players nets you gold to buy items. However, if you don't land the killing blow on an enemy minion, you will get ZERO gold, even if you've done most of the damage to it.

The faster you kill enemy minions, the faster the minions reach the enemy tower, which will make quick work of all non-cannon minions. It's better to keep the minion fights as close to the middle as you can; you only need to finish off the minion to get gold from it -- see if you can limit yourself to only attacking minions when you will kill them!

Tower Aggro

The enemy towers are dangerous. They have lots of health, armor, and a powerful attack that can quickly decimate low-level heroes. It's important, then, to know how the turret picks its target.

Enemy towers will always target allied minions first, switching to champions only if there are no longer any allied minions around. The exception to this is if you deal damage to an enemy champion, in which case the tower will immediately switch to the damaging champion, shooting at them until they die or move out of range.

Let me repeat that: If you deal damage to an enemy champion within range of the tower, it will immediately start shooting at you: You do not want this. Be very careful when attacking the enemy at their own tower.

Recommended Viewing

Four of these videos are a result of the Valoran Video Contest held by Riot Games, and are quick, 1-minute videos touching on just the basics (which seems exactly what you're looking for). The fifth video is made by Shurelia, an employee of Riot Games, and goes much more in-depth into what "Zoning" is, and how to take advantage of it.

There are a number of reasons this could be happening

1. You farm minions well instead of champions
2. You are getting the assist kills
3. You have the runes or masteries that boost your XP gains
4. The XP scales up over time so you will level faster the more time goes on
5. You get global XP for destroyed turrets

I am sure there could be more reasons, and also remember that 18 is the cap.. who is to say they would not be 20+ when you hit 18 if it didnt cap.