Of course you can! Beyond the basics of "Lights, Camera, and Action!", you really don't need much else. Daylight will do for lighting, take your pick of cameras, and have a story to tell. You don't even need sound. (It's been known to work before!)
If you want to make a film professional, then you need to have knowledge of what makes a professional film. That's what being a student is all about. Learn as much as you can about all aspects of movie making, and don't stop learning. It is fabulous to have the internet, and forums like this.
And then, as David said "Practice, practice, practice." Make mistakes, refine your skills, and shoot some more. Digital cameras are great for this. There are all sorts of work-arounds for when you don't have the best equipment. Experiment and have fun!
Kevin