Depends on context
>I recognise them, they appear approachable
Same thing I've done when seeing athletes and the like. Walk over, politely say "hi, apologies if you get this a lot but are you x? Just wanted to say I'm a fan of your work." and see where the conversation goes. Sometimes you get an "eh, thanks" and then cold shoulder, sometimes you get a good chat (I remember having a good conversation with Adam Gilchrist at the airport one day, we were on different flights but just shot the shit about music and 50s/60s test cricket). If they offer an autograph I accept, but never press them for it (one day of signings for a local gig a few years ago convinced me that autographs are best offered, not requested, can't imagine how mad it must drive some people who get recognised and get that shit every day). Note your appreciation, but don't engage the person on their field of work unless they invite it, people generally want to be able to section that shit away (and the ones who don't will make it clear by sperging about their own work as soon as the conversation starts).
>Recognise person but they don't seem approachable
Pass like ships in the night, remember seeing them however fondly/uncaringly as you want
>Person is at a public event in a professional capacity (unlikely for chuubas because of the nature of kayfabe for them)
I don't know what I'd do, I haven't attended a con for years. I guess the closest would be wrasslin' tours, in which case by a shirt or whatever to support the people you support, thank them for their service (lol), follow conventional rules of engagement, see where it goes.
>Ended up talking about surf and breweries with Juice Robinson for 20 minutes after a New Japan show
>He didn't know that the beer he was drinking all tour had a brewery/restaurant in a town he was going to check out the next day
Sometimes you can make the day of your oshi, just don't be a sperg and it will be fine.
