The biggest aid I have to extraction are 600 x 600 garden trays (Stewart is the brand I buy). They fit a super and I make sure I keep supers in these trays - any drips from the super either before or after extraction gets kept in the tray. I have four or five of them now.. I'd add that you need clear worksurfaces and jdeally a sink/water source to hand.
I have an uncapping tray that sits in a purpose made arrangement with a gantry with a hole in it for the frame lug ... catches all the cappings and any honey that drips. I've upgraded to a bigger tray so I need to re-make the previous arrangement in a larger size to take the new tray. The strip of stainless steel sticking out ? ... For cleaning the cappings off the uncapping fork/knife.
I also have a bucket filter to drain the cappings.
https://beekeepingforum.co.uk/threads/cappings-bucket.48558/View attachment 27653View attachment 27654
Organisation is the key and rather than having to clean up afterwards try and avoid making a mess in the first place ... avoid spill and drips - if you carry supers that might drip honey - carry them on a tray. Treat extraction like a production line. Set aside plenty of time and get well organised in advance - it's a chore but once you get going it's a very rewarding chore and for most hobby beekeepers it's only a couple of days a year and seeing the fruits of your bee's labour is one of the highlights of the season.