Once you hit the soft level cap in Destiny, you're going to need to know a few tricks in order to continue to level up your Guardian - this is where a little farming comes in to play.
Destiny guide: farming Legendary and Rare loot
To level beyond 20 you need to collect Legendary items. One method of grabbing Legendary armour and weapons is to collect Engrams in high volumes, and there's one mission on the moon in particular that lets you clear up lots of Engrams. There's no guarantee Engrams will unlock something Legendary, but collected in such volume it's a good chance you'll eventually get the gear you looking for.
The Moon: The Dark Beyond
What you're looking to do here is exploit a checkpoint in the game.
Once you've started The Dark Beyond, get to the point with the cutscene and the opening of the huge hive door. This trigger's a checkpoint and a tonne of Hive Thrall come rushing through the doors.
You need to kill all of the Thrall while ignoring the Knights and Acolytes. If you kill the Knights you'll trigger another checkpoint, and you don't want to do that. Concentrate on killing the Thrall when they are clustered together near the doorway - use grenades and specials to kill multiple targets in one go. They will drop Engrams and gear, and you should eventually get lucky with the drops.
Let yourself get killed by the Knights once the Thrall are dead and you will respawn again to kill more Hive. Repeat until you've got all the Engrams and gear you want. The loot dropped will remain when you respawn, so there's no immediate rush to pick it all up.
Remember: kill the Thrall in large numbers, grab the loot drops, let the Knights kill you.