To attack others you must not be in protection, you will select your squads and then click where you want to attack or move then hit the button at the bottom right corner to launch.
Smart phones with flash can play battledawn viewtopic.php?f=171&t=24117&hilit=How+to+play+BD+on+your+phone
is a guide on how to do so.
You will most likely be conquered but that is not a bad thing, generally people will leave you alone when you are conquered unless you have a crystal.
Good ways to increase your power would be to take outposts and raze them, take oil wells and metal mines which increase you income as well and worker income, and conquer other players.