You say you suspect you are on the autism spectrum. As someone with asperger's, I can relate to your sense of hopelessness and not knowing how to approach women and strangers in general. A few years ago I started my own business, and suddenly being introverted just wasn't going to cut it anymore. I needed to be able to make real connections with clients, suppliers, others in the industry, potential partners (especially as I started to expand and branch out). And that was just initially; these days there's also the firm that handles my advertizing, my accountant, reporters and radio deejays for interviews… just an unbelievable amount of business contacts. And that's not even getting into when I was running for State Representative, and all the socializing I had to do for that.
Here's what I did to overcome my introversion (even before I knew I was on the spectrum):

I spent a long time studying people, just watching them. At airports, at work, at concerts, in grocery stores and parks and clubs; wherever I was, I watched people and how they interact. I read books on body language and nonverbal communication. I practiced these things in front of a mirror then in my day-to-day interactions with teachers, coworkers, etc. And I noticed tremendous improvement in how long my typical conversations with people would last. Things went from being just an exchange of only necessary information to actual social niceties. People even began to ask me how my weekend had been, comment on a new shirt, things of that nature, which had never happened before.

I also practiced making and maintaining eye contact, which is a big part of nonverbal communication, but something I think of as almost entirely a category of its own because of how difficult this was for me initially. It was oddly easier for me to practice this with strangers than people I already knew. I would make and try to hold eye contact with waitresses when they were telling me about the daily specials, cashiers when they were handing me my change. I would try to make eye contact with people I passed walking down the street, and surprisingly, many of them smiled at me in return.

But these were all just superficial interactions. Where it really started to come together for me was when all my people-watching led to an 'aha' moment, and I started to think of myself as an actor of sorts. I realized that we all, consciously or not, spend the first part of our day, before we've even walked out the door, putting together the persona we are going to show to the world. You leave for work and perform your role there; you maybe meet some friends for lunch or drinks and perform an entirely different role; then you come home to yet another role. All our interactions are parts we play, little vignettes that comprise a play called life. Shakespeare had it right all along.

See, it was difficult for me to initiate and navigate conversations, but if I thought about it as a role I was playing, it suddenly became much easier. So I became a salesman, a businessman and a tradesman. I play these roles fairly well now.

But there is more to life than just business and work. About a year ago I started making a point of paying a complete stranger a heartfelt compliment each day. If I had to recommend just one thing, it would be to develop this habit yourself. There is no risk involved, because they are strangers. Compliment someone's taste in music (if it's playing where you can hear it), an item of clothing, a cashier's friendly smile. Take it a step further and ask for a small favor. Turn to a guy at the gym and say "Hey, bud. Mind spotting my next set? I feel like going heavy."

Yes, a guy. Notice how when I said to pay a stranger a compliment, I didn't specify women? That's because learning how to initiate conversations with women is exactly the same as learning how to initiate conversations with human beings. Take gender, sex, and attraction out of the equation. This will take some of the pressure off so you can build the skills and the confidence you need when you do decide to approach a woman you find attractive. And, trust me, she will definitely appreciate being approached as a human being rather than as a 'hot girl'.