If you draw monster hate while in a party, resist the temptation to run away - unless you have the ability to escape the enemy with a skill such as Frost Nova or Vanish.
Pay attention to which monster the tank is attacking - most of the time that will be the first target for the party's DPS to kill.
DPS classes need to watch their threat/aggro to prevent the monster from leaving the tank. Threat-reducing abilities such as Feint (rogues), Feign Death (hunters), Fade (priests) and Invisibility (mages) can cause the monster to forget about you and return to the tank. If your class does not have one of these abilities or it is on cooldown, you can also simply stop attacking momentarily.
Figure out a good ability rotation that maximizes your damage per second and uses a wide variety of your offensive abilities.