One great training tool for any drummer is a practice pad. These are small wood or plastic pads with a rubber playing surface. The pads are portable, much quieter than a drum, and are excellent for increasing your strength and accuracy while playing. Some practice pads have two opposite playing surfaces, a hard rubber side for strength training and a softer side for quiet practice. Try practicing rudiments on a pad while watching TV. You could even bring a practice pad with you to a performance and use it to warm up offstage.
Almost absolutely everyone has a dominant and a non-dominant hand. Research has shown that around 70% of people are right handed. This will translate into your drum playing and you will most likely be more skilled with one hand over the other. You may find yourself relying too much on your dominant hand. To become more limb independent on your drum kit, you will have to focus on practicing your non-dominant hand.
An easy way to train motor skills and hand eye coordination with your non-dominant hand away from the drums is to use your weaker hand in as many every day situations as possible. Try to use your off hand instead of your dominant hand for a couple of days for things like brushing your teeth, opening doors, or picking up objects throughout the day. Training your non-dominant side in every day usage will help you achieve better control with that hand on the drum set.
One of my favorite ways to practice is to play along to music I like. Being able to listen to music and pick out the drum beat in your mind is a great skill. Even while in a car or bus and listening to music, I often pick out the drums and focus on exactly how to play the beat. You can take this even further and use headphones to play along to music on your kit. I like to use the in ear kind, or ones with some noise cancellation, but any kind will do.
By training yourself to play by ear, you strengthen the connection between your mind and your instrument. It will become easier to make up beats in your head and then immediately play them on the drums.
Playing along to music helps you focus on keeping time because you can use the song as a metronome. Playing entire songs from start to finish can also be good endurance training, especially if you pick long songs. You may also learn some new patterns or techniques from your favorite music, something that you can then incorporate into your own original grooves.
Below is a clip of one of my favorite drummers, Chad Smith from the Red Hot Chili Peppers. Chad and Flea, the RHCP bassist, play a couple songs and jam together. Chad explains what he is trying to accomplish as a drummer in an improvisational environment and the important connection between bass and drums.