Firstly you will need to complete an assignment to unlock the SUAV. The assignment requires you to reach level 10 and to get a kill with the bomber which is available in the larger gametypes. To get in the bomber, I suggest waiting along with the crowd outside the white trailer until "Bomber deployed" shows up on your screen. Once you're in, simply get a kill. Try to shoot at stationary targets for obvious reasons, they're easier to hit. Once you get the kill, the SUAV should unlock.
When the SUAV is unlocked, I found the easiest way to get kills with it is to start up a TDM on Zavod as a lot of people like to camp on the rooftops which are pretty open. Wait until someone climbs up there, find a nice hiding spot and launch away. You should easily catch an unsuspecting sniper out.
Note: To kill with the SUAV, you need to roadkill the enemy which is simply flying it into them.