Instructions
Play your character like the worst villains from popular fiction who have no moral compass at all. Bad guys such as the Joker from the Batman series or any number of psychopathic serial killers from TV series can serve as good templates for a chaotic evil character.
Take what you want by force, and ignore any potential consequences that could result. The more even-tempered alignments might think twice about stabbing a cheating gambler inside the inn while several town guards are sitting at the next table, relaxing after their shift. You shouldn't bother to consider what will happen after your actions, but instead do whatever immediately gratifies your desires.
Always use the most violent or depraved option for completing a task. While the other evil alignments will have at least some hesitance toward certain actions, your chaotic evil character should have no taboos of any kind. If snatching a child from the home and sending the parents their kid's fingers one at a time is the easiest way to ensure the parents cooperate in your character's schemes, then that is what your character should do.
Disrupt well-laid plans and break up the foundations of civilization whenever you have the chance. A chaotic evil character will chafe against any sort of laws, restrictions or traditions that people insist he must follow.
Use the compunctions of good-aligned enemies against them. Put yourself into a position where a chaotic good hero is unwilling to kill you because you keep an even greater evil in check, or a lawful good hero won't attack you because you have rigged events so that your death will cause harm to all of the innocent civilians you are holding hostage.
Attempt to control everyone around you, whether directly or indirectly. If your character is a bloodthirsty half-orc warrior, you should try to subjugate your companions and any people you encounter by force. On the other hand, if your character is more of a sneaky thief who prefers a poisoned dagger thrust in the dark to take care of problems, you may want to simply play other people against each other or rule from behind the scenes.