To play the drums well, you need to be able to place any kind of note on or in between any beat with any limb independently from the parts played by the other limbs. A good way to start developing this ability is to play a basic beat and then vary one of the parts.
The following examples should help you become confident with varying your snare drum parts. Practice this type of exercise until you can play your snare drum on any combination of the 8 eighth note positions within a bar without losing the basic beat. This will give you great freedom to create your own beats and to improvise when playing with other musicians.
As a further development of counting parts, it is worth practicing singing what you play, firstly concentrating on one part at a time. To do this, you make an imitation of the sound of a particular drum or cymbal with your voice. For example, for the bass drum you could sing "bom", for the snare drum you could use "dut" and for the hi-hats you could use "tsst". These are only suggested sounds, so if you feel comfortable with others, use them instead.
Singing a particular part helps focus your attention on that part and whether you are playing it well or not. Try playing through a drumbeat three times in a row, first singing the hi-hat part, then the snare drum part, then the bass drum part. As you focus on each part, be careful that your other parts don’t become unsteady. To help things even further, it is useful to program your beats into a drum machine and sing each part as you play along with it. If you do this regularly, your time feel will improve dramatically.
To end this lesson, here is a drum part which contains several variations within the bass drum and snare drum parts. Practice each combination of two parts at first to ensure your coordination is strong and don’t forget the counting and singing techniques you have learned in this lesson.
Practice this example until you can play it through three times without stopping or making any mistakes. As you play, concentrate your attention and your voice on the bass drum part the first time through, the snare drum part the second time through and the cymbal part the third time through.