I'm not an old wood worker by any means was more of a metal basher and then a keyboard basher in the same trade, but since retiring taught myself sharpening tools for wood working
Firstly by hand on oil stones and leather strop and buffer wheel- but ended up with a convex bevel
Evolving to Secondly diamond stones, oil stones with honing guide leather strop and buffer wheel flat bevel and secondary bevel
Evolving to Thirdly Slow speed water grinder when needed to diamond stones, oil stones with honing guide buffer wheel flat bevel and secondary bevel
And finally evolving to belt grinder and bench grinder flap wheels - when needed then diamond stones, oil stones with honing guide buffer wheel flat bevel and secondary bevel
I use Lidl kitchen cleaner as lubricant on diamond stones, found it works well and will not rust
And generally use bench grinder flap wheels/buffer for carving chisels
The above is generally for chisels and plane irons
I restore old hand tools
Now for axes generally belt sander and bench grinder flap wheels
As others have said there is no right way only a way you want to do it