1) Join something where you'll see the same group of people regularly. A sports club, a restaurant job, a course, a workshop. If this is outside of your comfort zone, you should do it all the more.
2) Ask questions. You don't have to interrogate anyone, but if you're in smalltalk vicinity and they don't strike up conversation, ask about the thing you're doing (''so how long have you played tennis?''). If that conversation falls dead, ask them something else, like what they enjoy in their free time.
3) Answer questions. If you're not great at being social, this is surprisingly hard. You might think the other person doesn't genuinely care, but if they ask you what you do in your free time, don't just say ''idk I watch TV''. Tell them a bit about the movies and shows you like. It's well known that people enjoy talking about themselves, but there's a limit. If you're asked a question, they probably really want to hear it.
4) Try to remember their names, and use them. Instead of saying ''hey could you grab me a water too?'', say ''hey Robin, could you grab me a water too?''.
5) Remember things! This is probably my biggest tip. Smalltalk only lasts about 2 conversations. Whether it's exams or a bathroom renovation, ask them how that thing is going. It shows you listened and was interested in what they had to say.
6) Do people small favours. There's a thin line between becoming a pushover and being nice, which you'll have to figure out for yourself. But if someone mentions they have a headache, and you have Advil on you, offer them one. If you can take over someone's shift when they're in dire need, do it.
7) Don't be scared off when people don't respond warmly right away. They could very well have something on their minds which makes them come across uninterested. I usually give it 3 shots (preferably on 3 different days). If they actually were just uninterested in you, chances are that by the third time, they'll have warmed up to you. If not, leave it be. Some people are going to dislike you and there's nothing you can do about it.
8) Accept invitations! Invitations to things used to freak me the hell out. I'd think that they only invited me to be polite, or that if I would go, I'd mess it up. But you simply can't form a friendship if you only talk to people at work/sports club/course.
9) Don't be a downer. This is the biggest mistake socially awkward people make. A conversation can be about a lot more than what is bumming you out or why you don't want to go to the party.
10) Wise up. Experience goes above all else. You can't go 0 to 60 in becoming social and making friends. Be happy about every milestone. Maybe you'll accidentally ask a very invasive question, but at least you asked something!