I dont think our approach has changed much over the years, it's just become a lot less awkward lol.
We look at profiles that match what we are looking for, and if they are looking for what we can offer too, then we contact them. We chat via messages for a bit, see if we are all on the same wavelength. Usually we arrange to meet at a social, party, or club, but we have also met for drinks, or even a home meet.
At socials, parties or clubs, if the vibe is good, we will ask if they want to go find somewhere private to chat...usually things move on from there.