In general, women are not able to build muscle like men, strictly because of genetics and hormones. To become that woman on the left it takes years and years of training and HEAVY lifting, strict diet, and supplements (whether legal or illegal). The woman on the right accurately portrays what will normally happen to your body with a consistent training program and clean diet. So where do you find a training program? My recommendation, if you have never stepped foot into a gym, is to hire a personal trianer for at least one week, or five sessions. Not only will the trainer help you build a program that is specific to your body and your needs, he or she will teach you proper technique and help you become acclimated to the gym and the equipment itself.
If you've been going to the gym for a while and you're ready to get serious with your wieght training, I recommend going to a site like Livestrong and searching something along the lines of "5 day weight training for women" and you'll get a whole caboodle of results. If you're interested, here is my usual routine:
If I have time, I try to do 10-15 minutes of cardio as a warm up and I always end each work out with a 10-15 minute foam rolling/stretching session. On the fifth day, I try to to some kind of class at the gym such as BodyPump or spin. If it's a nice day, I'll ride 10-15 miles on my bike at home or do a "crossfit style" workout at the gym - just something to change it up a little.