Technique will differ from drum to drum, but there are a few things that most drums have in common. Most membranophones (drums) consist of a skin stretched across the mouth of some kind of shell. The shape and length of the shell will vary from drum to drum as will the type of skin used to make the membrane. The combination of the architecture and engineering along with the technique for playing will combine to create the drum's 'voice'.
Drums typically have three main sounds: a low sound (bass), a pitched tonal sound (tone) and a sharp, dry, non-tonal sound (slap). These three sounds make up the basics of playing most hand drums: djembes, congas, ashikos, bougarabous, doumbeks, tars, etc. Which ever type of drum you have, spend time playing it; practice the patterns you know or make up new ones, but whatever you play, try and do so with good clean sounds. Make your bass sound be as low and boomy as you can (make sure to tip it if it is on the floor so that the sound can come out). Play your tone so that it sounds clean and clear, but low enough to distinguish it from your slap. Play your slap so that there are no overtones (totally dry) and that it is crisp and distinguishable from your tone sound.
Plateauing. When you are practicing, play each rhythm pattern WAY slower than you want to. Really focus on the sounds of your drum and making them as perfect as you can. Hold your part at a slow tempo until you have played it perfectly for 3-5 minutes. Then, if you have held it perfectly for some time, increase the tempo SLIGHTLY and hold it at that tempo for a sustained amount of time. After holding it at the slightly increased tempo for some time, again increase the tempo a little bit, and hold it. Keep up this pattern of holding and then increasing until you come to the point where you are unable to sustain the rhythm pattern and quality of sounds. I call this system of practicing plateauing. When you can't sustain the speed or your quality falls off, go back down a few levels to a slower tempo and start again. Over time, with instruction and practice, you will be able to push your edge of ability to a point where you will be able to sustain your quality of sounds at a fast tempo.
Find a good teacher you can work with to help you with technique and rhythmical sensibility. It will go a long way towards increasing your enjoyment of drumming.
jm
