Enroll in an ASL class at your local community college. Check with the National Association of the Deaf and see if they offer any classes or host events in your area. The Association for the Hearing Impaired also regularly offers classes in ASL.
Advertise --- in your local newspaper, on the community notice board or on the Internet --- for an ASL tutor. Ask your friends if they know anyone who could teach you the art of "speaking" ASL.
Start with the ASL alphabet. Watch YouTube demonstrations of how to spell the letters in ASL. Practice spelling words as you walk around your house, such as sofa, window and door. Practice your ASL every day and try to improve your speed.
Watch television stations that have hearing-impaired translators in the background. Turn down the volume so that you have to get the information through your eyes.
Find a friend who also wants to learn the art of sign language and practice with her. Learning any language requires practice, and you can encourage each other. Put a piece of tape across your mouth or a small ball in your mouth so that you can't talk.
Find out where the hearing-impaired people hang out --- it could be a club or a local café --- and join them. Explain --- in ASL, of course --- that you want to practice the art of signing.