For at least 20 years I've washed mine with washing up liquid, and more recently baby shampoo (because it contains no alcohol - although the alcohol in washing up liquid is so low in concentration I'm almost certain it makes no difference anyway). Until a couple of weeks ago I just used to blot dry with a towel, then kitchen paper, then air dry.
I'm now using a very simple vacuum drying system which has REALLY surprised me with how much cleaner it gets my 78s, both visibly and audibly, by sucking more dirt out of the grooves. Honestly, it's been an absolute revelation. I don't have the photos to hand now but I posted them here (hopefully this is the right page, or if not, it's page 6 of this thread):
viewtopic.php?f=18&t=44380&start=50 Professional-style record cleaning for peanuts!
Despite seriously respecting Percy Wilson's work, I am resolutely against putting oil in the grooves. I doubt that washing with soap will get it all out again. Back then, I doubt he would have been thinking about very long term effects and (from my former life in plastics and rubber chemistry) I think there is likely to be a gradual interaction between the shellac and other resins in the record compound. The oil may give a 'helpful' lubricating effect in the shorter term though, plus I find when cleaning records they sometimes sound a bit 'edgier' at first - I believe the accumulation of dirt was probably filling in microscopic damage and/or unwanted crystalline projections in the groove wall (whether exposed by wear or caused by microgranulation) and sometimes a play or two with a steel needle on a good machine is necessary to "settle them down" again, before a thorn or fibre needle will work, or a modern 78 stylus will sound best.