Disassemble, clean, dry. After that I've used whatever grease is on hand with good results. In my personal ratchets I used Valvoline Synpower (#2) grease, at my old job I used Mobilgrease XHP 222. Both work well, as would any old grease.
The difference in smoothness is excellent - it made Snap-off feel like Craftsman, Craftsman feel like SK and SK feel like Snap-on. I still have to wipe a bit of grease off now and then but I'm a weekend warrior at best.
My Snap-offs are only for light duty home/junkyard use; the Craftsman is 10 years old an still works like new. Better than new after a good cleaning & regreasing!