That's exactly what I started out with. Shoot little clips around the house, experiment with lighting (indoor and outdoor), experiment with moving the camera (and potentially build a simple rig -- all you need is a piece of wood and a bolt!), experiment with the different focal lengths and apertures on the lens.
Learn how to use the histogram while shooting video (that was a HUGELY useful tip given to me by somebody else on these forums). And DON'T forget to see how all these videos look on the larger computer screen. You'll be shocked at the differences between the on-camera screen and a computer monitor.
These are all things you could/should be doing to start out. Learn to use the camera so well that it's intuitive, and then you can then start to worry about what is in front of it. Other recommended reading is the NoFilmSchool DSLR Cinematography Guide: http://nofilmschool.com/ (there should be a pop-up that will allow you to download it for free). It's basically the ultimate beginner's how-to.