Cover your entire body in plastic, except for your hands (wear gloves, duh). Do not walk on any surface that isn't hard, and avoid any particularly dusty floor or any floor with a substance on it that could leave a print. DO NOT GRIP ANYTHING TOO HARD. As for getting rid of the body, dissolve it completely in acid, then dump all that shit in a river or something. Get rid of the plastic you wore when you killed before going back home and clean your own house.
Or you can open all of the windows in the apartment (remember, no prints of ANY KIND, including ear, lip, etc.) and leave the corpse there. If it's winter, the time of death will be a lot harder to determine. Kill the person with an icicle, so the murder weapon will literally melt away.
Oh, and in the struggle, make sure to touch the person as little as possible, because the gloves can be identified by contusions. Or, if you use a gun, do something that would alter the signature of the inside of the gun barrel, so that when ballistics analyzes the bullet from the body, the mark on it will not match any that will come from your own gun.
Wipe away all blood, too, thoroughly, and make sure the blood does not get on surfaces that will absorb it. The spatter will allow the crime scene examiners to gain more insight into the struggle and the cover-up.
If you get rid of the gloves immediately afterward it looks suspicious. Just keep the gloves and make sure that nothing is left at the scene that can identify them.
I felt too lazy to quote the previous posts since I'm only on here for a short period of time. This is just my two cents from studying forensic science in school.
