I have this problem too. I absolutely svck at conversation, and everyone always comments on how quiet I am, but I've become WAY more social and talkative in the past year or so.
My honest advice? Stop giving a [censored]. Yeah. That's all I got. Just stop caring what people think, stop over-thinking what you should or shouldn't say in a conversation, and just say whatever comes to mind and realize you won't be judged as harshy as you imagine yourself being judged and even if you do, who cares? You don't care, and you know why you don't care? Because you stopped giving a [censored].
That's probably bad advice, because I reached that conclusion by less-than-pleasant means, and not caring seems like a bad thing, but hey, it works for me. I talk more now. I feel more confident now. It might be hard at first, but practice, and once the world doesn't end the first few times you throw yourself out there, it'll come easier each time.
Or maybe none of this applies to you and you are anti-social for completely different reasons than I am.
I can go with this. When you stop worrying, things just flow easier. Of course that easier said than done. I read somewhere once that "they aren't thinking about you, they're thinking about themselves, just like you are right now". That always comes into my mind whenever I worry about how I'm coming across to someone new, because they've likely thinking the very same thing about themselves.
A good tip I found helped was reading the news. There's always something going on (what may be the main interest might be dependent on your age, social group or interests), and so you'll normally have something to bring up if the conversation lags. But if you do this, it might be best to stay away from certain "hot topics" that tend to polarise people. The forum rules here are a good example of what may or may not be suitable to bring up in casual conversation.

The best thing is to just keep on at it though. I reckon everyone here has had an awkward conversation with someone, had a faux pas or said something that they wished they hadn't. But once it's done it's done, and you learn from it and end up more confident in yourself because of it. I've found that generally people are pretty nice, and aren't going to ostracise you because you might be a little awkward. Some people even find it endearing.