|Don't know how to make a variation? Any of these|
could be a variation of the first beat. Why not.
Play it over and over again.
Normally when someone writes out a beat for you, they only give you one measure of it, but it is a time feel, and it's meant to be played over and over as background to a piece of music, so that's the way you should practice it— repeat it many times without stopping.
Learn to start and stop.
It's a common thing for a lot of beginners to start playing a beat with one limb, and then add the others. You won't be able to do that when you're playing with a band, so take a few minutes and learn the first four or five notes of the complete groove; once you can play the first four or five notes. Also learn to end the groove cleanly on beat 1, with the bass drum and cymbal (whichever one you happen to be playing at the moment), or bass, snare and cymbal together.
Make a phrase
Begin thinking in two measure phrases. You don't have to do anything differently, just be aware of an A measure, and a B measure. You can hit the crash cymbal at the beginning of the phrase if it helps you keep track. As you are more comfortable with the groove, you can begin improvising fills or variations in the last measure of the phrase— or in the second and fourth measures of a four-measure phrase.
If you're not hearing any obvious variations on the groove, try just making a small change to it— add a note, or leave one out. You may have to plan it out in advance at first, but soon you'll get a feel for how to do it on the fly. See the graphic for examples of possible variations.
Continued after the break:
Vary the tempo
Try it a little slower and a little faster than you are completely comfortable with. Do play reasonably realistic tempos for the style— there may be value in practicing excessively slow or fast, but that's a different thing than what we're working on here.
Vary the dynamics
You don't have to systematically go through all your stuff at every volume level; just change your volume once in awhile, and maintain that level until you decide to change it again. Where most people get caught flatfooted is when they have to play softer than they've practiced, so don't neglect that.
Play the groove with the right hand part on the hihat, ride cymbal, cymbal bell, floor tom, cowbell, floor tom rim, or whatever you have handy that seems appropriate. Play your left hand normally on the snare drum, or on a tom tom; or as a rim shot, or a rim click; or you can move it between whatever sounds you can reach easily. As you move to these other sounds, you may want to vary the parts, or the accenting of the parts, to be better suited to the instrument— just follow your ears. Beginners, just practice moving your right hand smoothly from the hihats to the ride cymbal. These types of changes to the groove suggest different sections of a song, so you can play 8-to-many measures of each voicing you practice.
Again, you don't have to cover every possible combination of sounds with every single beat you practice; you do want to know what are the different sounds available to you, and be able to move smoothly between them, and possibly make adjustments to the pattern to suit the sounds you're playing.
Clear away the junk
If it's a very busy groove, calling for a lot of specific little things, try paring it back— lose the filler/“ghost” notes on the snare drum, the open hihats, whatever.
Or you can add those same sorts of things to a groove that doesn't have them. You'll get some ideas for that as you listen and play more, and work through more practice materials.
So that ordinary page of rock beats has now seemingly mushroomed into an immense extra practice burden, but don't be overwhelmed. You don't need to do all of these for every single beat you practice, and you may not be able to do some of them at all, at first. But just be aware that these are the normal parameters for what you do with a beat in playing creatively, and in doing your job as drummer, and you'll be able to do them over time.