How to level up fast in Clash of Clans?

The more upgrades you complete the more you will get experience points which can help you level up fast.

The more you upgrade your town hall the more experience points you will get and the faster you will level up.

When you donate troops to the people in your clan you can level up. Some players recommend joining a new clan every now and then so that you can donate more troops fast. See how to defeat clan castle troops.

When you complete an achievement you will get some experience points. The number of points you will get is written beside the achievement in the achievements table.

When you destroy the town halls of others you get experience points. The more you attack others aggressively the more you are likely to gain experience points. 

On the single player map, destroying a goblin town hall also gives you experience points. (See How to tell if Clan Castle is Full in Clash of Clans?)

When you clean obstacles you also get experience points. Clean up obstacles fast to get more experience points. 

When you gather more resources fast you will be able to make upgrades faster and as a result you will level up faster.

Use gems whenever possible to force the upgrades to complete fast. This will help you gain experience points fast and so level up fast. (See How to find and repair the gem mine in Clash of Clans?)