Not by striking up conversations with strangers!!
On tumblr, a lot of my mingling happens in fandoms -- I talk about my headcanons or draw my favourite characters or silly quick doodles of them interacting in ways I imagine would be fun. I don't often reblog things, so like 90% of my interaction just comes from putting my thoughts out there and responding to the people who respond to me.
On twitter, I might talk to someone if they're talking about something that I agree with or am curious about, but most of the time I don't jump into conversations with people I don't know. I'll engage with things like #webcomicchat, which does feel like a big conversation, but I'm not coming up with things to talk about -- the main account is asking "what do you guys think about X?" and we all put in our two cents, and maybe respond to other people who have interesting thoughts.
I'll also try to respond to things I like -- if I'm reading a webcomic and following the creator on twitter, I'll definitely tweet at them if I love a page and it made me feel emotions. Sometimes creators respond to things like that, and sometimes they don't.
I've never tried to "keep a conversation going" on twitter, and if someone else did that with me, it would honestly be a little weird!! It's usually more like, they tweet something, I respond to it, they respond to me, and that's probably it. I don't think I've ever "struck up a conversation" with a person I didn't know online, and I'm honestly prettty cautious about responding to things if I'm not sure that I'm the audience for it. I think those qualities don't have to be awkward -- being thoughtful about how you interact on social media, and not assuming everyone wants you jumping into a conversation if you don't know them, are pretty socially adept qualities!! You can still engage with social media without losing that thoughtfulness.
I lean more on finding conversations that already exist, and joining in those conversations (and fandom is really just another kind of conversation). I'm sure you can get good results by being the kind of person who's unafraid to run up and introduce yourself and strike up conversation, but it's definitely not the ONLY way to mingle.