What is the easiest way to stop a door from catching on the floor?
If the condition has developed over time, you can try tightening all of the screws on the hinges.  If any of the screws keep turning then you can replace them with longer screws so that they grip the stud behind the frame and pull the door up.

If you recently installed carpet or a new floor then you will need to plane the bottom of the door with either a hand planer or by sanding.  There is also a planer attachment for the dremels which works pretty well for light jobs, and in some cases you can even do it without removing the door.