Drum beats are most often attributed to rock styles. The difficult thing when trying to mimic these styles is that they are HIGHLY produced. Many rock songs incorporate a very simple drum beat but run that track through several compressors, EQs, verbs, and many other effects to make it sound "big". So it may not be much in the performance of the drums as much as it is in the recording and production of it.
That being said, start with something simple then add in some pickups. Here's an example: start with something that is very 8th note oriented then add 16th or 32nd note pickups before the snare hits on two and four. Also try varying the hi-hat or cymbal pattern by adding some swing type notes (dotted 8th - 16th pattern or broken triplets)
See if that gives you a start. My background is in jazz and rock drumming, so I can give specific help if you need more.