Finger drumming

If you don't have access to a drum kit, then there are lots of other ways that you can create beats.  Apps like band lab or sound trap can be found online and are a pretty fun of creating loops.  You can also use apps on your phone like real drum or garage band  if you have an iphone or ipad.  Playing on a tablet a bit  easier as you have a bit more space to play with but you can still create some pretty cool beats using your phone. 
The below video shows you how to play the fist 16 eight note rock beats from Essential Drum Beats' level 1.  

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And with a bit of practice this is what you can do