Dilithium is a reward/currency which is earned by a number of missions primarily and Duty Officer assigments secondary.
It can also bought on the player driven dilithium exchange for Zen (Perfect's World real money currency)
At low levels you don't really have many opportunities to earn dilithium. More opportunities will open up at higher levels, don't worry.
At lower levels, you don't really need it yet.
The gear you loot should be mostly enough for the leveling process.