Most of the fundamentals of shooting are essentially functions of hand/eye coordination, and most of them apply equally for women and men. However, there are some elements of shooting that go way beyond your contact with the gun's trigger and grip. Specifically, what about your shooting stance? Is the proper shooting stance different for women than it is for men?
In this video from Smith & Wesson's excellent GUNSMARTS series, pro shooter Julie Golob illuminates her stance on ... stance. Although there are several different very specific "poses" that shooters will assume (you'll hear terms like Weaver stance and Isosceles stance bandied about), your primary concern is stability and recoil control. What you're trying to do with your stance is to bring your weight up onto the balls of your feet, lean forward into the gun and use your body's weight and construction to absorb the pistol's recoil.
For the most part, this looks very similar for women as it does for men. That said, a woman's body is almost always going to have a lower center of gravity than a man's. That's not a bad thing at all; you can think of it as Nature's way of making us stable, and it may actually make assuming a good stance easier for you. Take a look at this terrific video for more surprisingly intuitive and easy-to-assume pointers on your best shooting stance and grip!