Similar to this for me except we've got microfiber cloths for glass (they're almost like a silky finish as opposed to the pile finish on a regular microfibre, and the finish on each side is slightly different) I dip one in hot soapy water, wring it out and clean the telly, dry and buff with the other one. My telly doesn't really suffer from vape residue, more small handprints etc from the kids, but the windows are bad for it in winter and these cloths are absolutely brilliant for cleaning glass (as you'd expect as that's what they're designed for - I've not used window cleaner since we got them, hot water with a bit of fairy does a better job on windows/mirrors/car windows/telly to me, and no streaks)
Before those I used baby wipes and toilet paper/soft kitchen roll to dry, and a buff with a standard microfibre on the telly.