I am going to be specific here.
Learning to be a good conversationalist is somewhat art, but mostly just a skill. that can be learned.
Take a course in public speaking, there are likely ones in your area that won't be expensive. Talk about getting out of your comfort zone! This will move you faster than any other solution.
Get a video camera or your phone and vid yourself reading a book, the morning newspaper, or anything that gets you to speak.
Strike up conversations with ANYONE that interests you. Other women, the bartender, the sakeswoman, a waitress, person in line at the grocery store. Not easy, but in talking to other women, or non sexual circumstances with men, you will get better.
Be truly interested in learning something about the other person. Truly. Guys screw this up in chatting up girls a lot by talking about themselves way too much. Not to be too boastful but I can chat up attractive women with ease and get to phone numbers or bed quick mostly because i never talk about myself. I know me, I want to know YOU, and that extends to everyone, my mechanic, the plumber, the bartender, the guy having a beer next to me in a sports bar, and eventually the hot girl looking to dance in the club to whom I am attracted. However faked interest is easy to detect, be genuine, if the woman next to you has a cool haircut or really well done nails, ask her to whom she goes.
Talk to your mailman/woman. Force yourself. Work out at gym? Ask people about their workout plans and goals, particularly other women.
I was the geek in high school with the zits, no game, awkwardness and shyness you could cut with a knife. I did most of the above and now talking to people is just plain easy.