Mix it up. Using one kick drum sound and one snare drum sound over and over will be a dead giveaway that your drums are not real. Pick out a few different kick or snare sounds that are similar but not identical. Also use different configurations of drum sounds, such as open, semi-open and closed hi-hat sounds to add interest to your drum tracks. Consider using a kick drum sound from one drum kit and a snare drum sound from a different kit.
Change the velocity. If all of your drum hits have the exact same level, they will not sound real. If you are using a MIDI keyboard or controller pad, use different pressures when playing the notes. This will create dynamic differences in the velocities of the drum notes. If you are programming your drums through software, use the velocity adjustment in the software to add realism.
Make your rhythm slightly imperfect. Rhythms that are inhumanly perfect are possibly the biggest indication of electronic drums. If you are using software, try using a swing setting to make the drums groove a little better. You can also move the individual drum hits slightly so that they do not line up with the beat precisely. Be careful not to overdo the imperfection, or your drums will sound sloppy.
Adjust the envelope of your drum sounds. The envelope is the timing characteristic of your drum sounds. Electronic drums often sound choked. Adjusting the attack and release of the drum sounds can open the drums up and make them sound more natural. Also consider adding a little natural reverb to make the drums sound fuller. Avoid unrealistic or gated reverbs, as these make the drums sound more electronic.
Put yourself in the drummer’s seat. If you want your electronic drums to sound realistic, don’t do anything a real drummer couldn’t do. Remember that a drummer only has two arms and two legs. A real drummer cannot hit three toms or three cymbals at the same time. Likewise, a real drummer cannot operate a double kick drum pedal and a hi-hat pedal at the same time. If you are using a double kick drum sound, you need to be sure that your hi-hat sound is open.