Attacking is the best way to get experience, and exert your superiority over those weaker than you. In order to attack you need 50% energy, at least 50% health remaining and you should also have your weapon of choice equipped. You initiate a fight by clicking of the Attack option of your intended victims profile, and then its simply a case of clicking on your weapon to start an attack round. Make sure that you really want to fight the person, because once you start you can not do anything else until either one of you loses or you decide to run. If you win a fight you will get a choice to Leave, Mug, or Hospitalise them. Each option has its own merits;

Leave Them: Selecting this grants you a percentage of experience depending on how much stronger you are compared to the person you are attacking.

Mug Them: Selecting this grants you a percentage of experience depending on how much stronger you are compared to the person you are attacking.

Hospitalise Them: You would select this if you really do detest the person, or feel you need to exact some real revenge, as this will extend the victims hospital stay quite dramatically.