I have been asked this so many times that I have finally kept a copy for this. My sharpening thoughts and method are derived after 60 plus years of woodworking. It pertains to carving tools which have to be the very sharpest, but relates to all sharpening.
Carving tools must RAZOR sharp! Even the best carving tools are never really sharp enough when purchased. So you must learn to sharpen until you can literally shave the hair off your forearm. Yes, this is the actual final test.
As to "stones", everybody has their preferences and in the end they all seem to work. The object is to use the coarsest "stones" to shape the blade and bring it to a sharp edge. Then you begin polishing the edge until it is a mirror finish. In the process a "wire edge" will be produced that will bend/break off. You have to get rid of this. The best way I have found is to jab the blade edge into the end grain of a piece of wood. This knocks the wire edge off to get you back to solid metal. So work your way sharpening through finer and finer "stones" (three is usually enough) until you get to that "almost" razor sharpness. Then you finish up with "honing" with super fine abrasive in a leather "strop", polishing even more. Stop every so often between "stones" to remove as above any wire edge that has formed. Test by shaving on your forearm. If it isn't sharp enough, go back a step or two and repeat. Once you have a razor sharp blade you will only need a quick strop from time to time as you work.
My preference for "stones" (I write it this way as old fashion actual stones have been replaced by more modern grits like diamonds, etc.) is to shape the rough and abused blade with a coarse diamond sharpener. This works fast but leaves deep scratches in the steel. You then have to begin remove these scratches by polishing the steel. You can use finer diamond "stones', water stones, carborundum stones, Arkansas stones, etc. to do the polishing. I use finer diamond stones for this. Then I move to Arkansas stones to finish the sharpening before honing. I prefer Arkansas stones as they work well and stay flat over time, unlike water stones which are very soft and wear. These have to be "flattened" periodically.
I have found that being able to actually see the edge under magnification is a great help to knowing how you are doing. I use a cheap Harbor Freight 2x (power) lens visor to do this. The trick is to view the edge straight on using a very bright light. If the edge is not sharp, you will see the edge as a thin bright strip of light reflecting off the edge. If the edge is sharp there will be no light reflecting off the edge.
I make my own leather strops to various shapes and sizes using leather bought from Tandy leather supply (
https://www.tandyleather.com/en/). You have to embed the leather surface with a fine abrasive. This can be bought online from most of the woodworking sources. Personally, I use Turtle Wax car polish for this.
And while we are on "sharpening", don't forget the use of a sharpening "steel". These are the round things you often see fancy chefs use on their knife when cutting a roast. These are round in shape and have fine grooves like a file. What happens to a razor sharp edge, especially a narrow one, it the edge gets bent some to the side in use. The steel straightens out the edge. It only works with an already sharp edge so it can be classified as a type of hone. Great things! I use a little one on my cutting edges.
Sources:
https://www.sharpeningsupplies.com/Carving-Tool-Sharpening-C30.aspx
As for the use of a Tormek type sharpener, I simply modified a Harbor Freight powered sharpener that uses a water cooled wheel with a Tormek type blade holder. The strange black thing on the left is the blade holder, a junk part of a medical device I found and cut down. You can make the same with some wood, a hinge, and a hold-down of some type. Works great!! Good for shaping and sharpening, but you still need to hand polish and do some final polishing and honing.