There are many targets you can attack on the world map. First, make sure you have enough troops to attack with, then head to the world map, pick your target, and click on attack! 

If you have the target coordinates (X, Y) you can put them in the box with the magnifier at the bottom of the world map screen. This way, you will be transported to the desired location and attack your target. 

Important targets you can attack on the world map
-Other players’ bases. You can also attack the players who attacked you by clicking on their coordinates in the battle report you’ve received in your mail to be transferred to their location. Keep in mind that if the player has already changed his location, you will be transported to his old location.
-Resources fields: if a player's troops are collecting resources from a resource location, you can attack him and occupy that location if you win the battle.
-Rebel forces.
-Rebel camps.

And there are many other locations you can discover as you delve deeper into the game.

Important notes:
-It is recommended to scout your enemies' bases or resource locations to find out the number of their troops and other important information that can help you plan and attack accordingly.
-You can't attack bases under protection or members of your alliance.