This is something I am trying, I've tried some different things. The Meetup website is a good place to perhaps look for suitable events or groups, but has been hit and miss for me. The first time I went to a meetup it was a gig and the organiser didn't even turn up and I didn't meet anyone, it took quite a while to find the motivation to try again.
Last week I went for a group walk, I really enjoyed that as I did manage to talk to a few people, and if I wasn't clicking with someone or other I could always drift away to look at something interesting, or otherwise extricate myself and try chatting to someone else and I like walking so it was OK and didn't feel too pressured.
Tonight I went to a group meal, it was with the same group, as they put on quite a few things, unfortunately it all went a bit wrong from the outset, really. I was doing well and talking to a person I seemed to kind of click with and felt OK with, so I sat with them, then for some reason the group organiser didn't like the balance of the table and made me go and sit right at the end in the corner, where I felt stuck with some people I couldn't really make conversation with. They were nice enough people but were there to practise their English language skills, which is fine, but I struggled to hear them and they struggled to understand me so I started to feel quite disconnected. It was an all you can eat buffet sort of deal, I spent a lot of time escaping to the buffet, which was an ordeal in itself having to escape from my tight little corner... And then I started feeling misanthropic towards the people piling their plates with food and barging in front of me as if the huge volume of food was going to run out.
We then went for drinks and I ended up in a mini group of 3 the other 2 of which already knew each other for years and so I started to feel myself disappearing as I always do in any situation that isn't 1 to 1. Put me 1 to 1 with someone and I am fine, but the larger the group becomes, the more uncomfortable I am (typical INFP really!). And again somehow the person I'd got on with and spoke to again on the way to the bar ended up sat somewhere else, sigh.
I tried a running club for a while, but I think a lot of the people were far more interested in running than talking, so I kind of drifted away and have gone back to running on my own, which I enjoy.
I've pretty much given up on ever finding a partner, but some new friends would be good.