There are a number of options. I prefer to always put wiring in conduit, as we have lots of shale rock in our ground and a lot of clay that makes our ground very hydraulic here in Western PA.
There is direct burial cable, too.
I'd suggest you take a trip to your local Lowes/Home Depot/whatever and talk to the electrical guy. Often they are older, retired electricians. If they are young and don't sound like they know what they are talking about, don't listen to them
We are about to run both electricity and water to our coop(s). We are going to put a switched pedestal next to our building (garage) with GFCI and the underground wire in a conduit that will run to this switch.
This way, you'll be GFCI protected, can turn off power to the coops at any time with this outside switch, and even add an outdoor receptacle at the pedestal for outdoor needs.
Codes are funny around here. I remember one time an inspector complained because I put 'direct burial' cable in a conduit!
Another interesting note: Around here, if the electrical line isn't 'permanent' (ie you can unplug it), you do not need an inspection as it is considered a big extension cord. You should ask a local electrician/inspector before doing any of this work, though.
We're looking just to run small light, maybe a water heating circuit (to keep the waterers from freezing, NOT a water heater

), and maybe an outdoor motion detector light to chase away predators. Nothing big.
The distance you want to run this line also makes a difference in the size of wire you need. Longer runs need larger wire.
Hope this helps.
- JC