Use a stud finder. This is the simplest, most effective way to find studs. By sliding the stud finder across the wall, the stud finder will beep and/or light up when it crosses a stud.
If you don't have a stud finder, there are several methods that can be effective in finding studs. When a home is framed, the wall studs are usually spaced 16 or 24 inches apart. If you start in a corner and measure out 16 inches and you don't find a stud, you should find one at 24 inches.
You can also try holding a flashlight against a wall and looking down the wall to see if you can tell where two pieces of drywall meet. At that intersection, you'll definitely find a stud.
Look for light switches and electrical outlets, too. Those are usually mounted on the side of studs, so that's usually a good starting point for finding them.
When you think you've found a stud (if you're not using a stud finder), confirm it by driving a thin finishing nail through the drywall near the baseboard to see if you hit a stud.