When it comes to doing more pullups, the way to do it is to keep doing pullups. That might sound oversimplified, but there's more to it than simply getting up on the bar and trying your best. By getting methodical about your routine and adding in some other beneficial exercises, you should start to see results within a few weeks or months.
Perform a short warmup by walking or jogging for about five to 10 minutes. Do this before every workout to provide your muscles with the oxygen they need to perform properly.
Stand in front of the bar and place your hands on the bar about shoulder-width apart in an overhand grip. Tighten your abdominals and pull yourself up, reminding yourself to incorporate your latissimus dorsi -- the muscle at the center of your upper back, to complete the move. Stop when your chin is just above the bar. Lower your body down, not touching the floor, and then do a second repetition. Do as many pullups as you can and write down that number in your training journal.
Repeat that process every other day, doing as many pullups as you can as the first part of your training process. Following that, do two sets of other types of pullups, depending on what's available to you. If you work out in a gym, use the assisted pullup machine. Displace as much weight as you need to do two sets of 10 pullups. If you have a playground nearby, use the lower horizontal bars to do feet-on-the-floor pullups, again displacing some of your weight.
Start a cardio routine, if you're not already doing one. Losing body weight is one great way to increase the number of pullups you can do, since a lighter weight means less weight to pull up against gravity. Run, cycle, swim or do any other type of cardiovascular exercise at least three or four days a week for 30 minutes, helping you burn the calories necessary to drop pounds.
Do strength-training exercises that work the muscles necessary for pullups. For the latissimus dorsi, use the "lat pulldown" machine at your gym. For the biceps, do biceps curls. For the chest and upper body in general, use the dip bar, or the assisted dip bar at your gym. Do two sets of 10 repetitions for each exercise, three days a week.
Install a pullup bar in the doorway of your home. Whenever you pass through it, do a single pullup.
Keep tracking the number of pullups you can do in that training journal. If you stick to a routine that includes pullups, strength training and cardio, it's likely that you'll slowly increase the number of pullups you can do.