Home runs aren't just hit by the top softball players. While it is important to have and develop the proper skills, it is also true that the right pitch, the right swing, the right bat, and the right frame of mind must all come together to increase the likelihood that a person will hit a home run in softball.
Wait for the right pitch. Depending on what kind of softball is being played, you will want to wait on different kinds of pitches. If you are playing competitive scholastic softball, all the pitches are going to come in at a fairly high rate of velocity. Wait for the right pitch in the right area. The best area for the softball to be in to hit home runs is in the middle of the plate, about thigh high. In slow-pitch softball, the best pitches to hit are usually just above the waist.
Swing for contact. A person who comes to the plate intent on hitting a home run will find that her swing is somewhat unnatural, because she is overexerting herself. Swing naturally. Although having power in the swing is important, it is equally important to have a level swing that makes contact with the ball over the plate.
Increase bat speed. Because the pitches that are most likely to become home runs are those that are thrown hard, you'll need enough bat speed to get the bat around quickly enough to connect with the ball while the ball is over the plate. A person who is getting around on pitches just a tad late should try a slightly lighter bat.
Improve capacity for power. While the speed of the bat is important, the mass of the bat is important as well. The heavier the bat, the farther a ball being struck by it is able to travel (assuming the bat is swung quickly). There is a balance between bat speed and bat mass that a softball player must find to determine what suits her best. The best way to determine the best bat is to simply try out different kinds.
Follow through. After swinging, do not stop halfway into the follow through. Allow your arms to end up next to your ear before releasing the bat. A person who follows through is able to generate more bat speed and increase the velocity at which the mass of the bat is traveling, thus causing the ball to pop off the bat.
Keep practicing. The most important thing is to practice hitting in general. As a softball player practices hitting, she will get a better idea of the things she needs to do with her swing to generate enough power to hit a home run in softball.