Simple :)

You need to:
1) choose your city, where you have soldiers
2) go to view of the world
3) choose an island, where you are looking for a target
4) click on your target
5) in left menu you have "pillage".
6) wait for battle :D

Thats all :D

However, if you are asking how battles works... hmm... Who knows that? :D I havent even found in board informations, how battles go :/