I'm lucky in that I don't have many of the social challenges many other Aspies face, so perhaps I can give you some input from the other side of the "wall".
If you're an adult, one thing you should know is that the older you get, the harder it is to make new, good friends, especially if you aren't married and/or don't have children. I know plenty of NTs who struggle to find real friendships in adulthood, too. So make sure you're not too hard on yourself. You're by no means alone.
Before you do anything else, you might want to give some thought to what you want in a friend, what your boundaries and preferences are for interpersonal interaction, and what you would like to do with a friend you might make. The answers to that will give you some ideas of where you might want to look to make connections.
To help overcome your difficulties with socializing, Google it. Literally. There are some great websites like this one, designed to help people who are socially awkward:
How To Be More Friendly And Social | www.succeedsocially.com .
Once you've studied up, one good way to put yourself in situations for natural conversations that may lead to friendship is by joining a group of some sort, for which people congregate to share a particular interest. That gives you something to talk about that is almost sure to be welcomed by your conversation partner. If it doesn't go well, no harm no foul. You never have to go there again.
The bottom line is, making real friends takes a combination of effort and luck. Getting the framework for the effort down will improve the quality of your effort, but don't feel bad about yourself if it takes a while to find someone you click with. Some people attract others in droves, it's true. That doesn't mean there's a single true friend in the bunch. People tend to like me a lot when they meet me, but only a very small percentage of those people are anyone I would really want to know.
Edit: Here's a thought. If you don't mind people knowing you're on the spectrum, be open about it with new people you meet. I have an Aspie friend who actually tells people he has Asperger's when he introduces himself, and says "So if I seem a little awkward, that's why." I'm amazed how many people respond to that by wanting to talk to him, if only out of curiosity. He has a ton of friends so something in his method must work!