After the foundation shaping, sand and work only by hand. You want some type of "paste producing" polishing technique. Do not sand/polish dry. Do not use a grinder or buffer.
Hand sand the blade to 1000 grit, and then etch with 10:1 FC or 100:1 nitric acid. Wear rubber gloves, and dab the etchant on with a cotton ball. "Rubbing" in the hamon with your finger tips. Rinse and take to 2000 grit. Repeat the etch. Take to 4000 grit and etch again. Take to 8000 grit, etch lightly, and polish very gently with Flitz. Don't rub the hamon any more than necessary. On a very finicky hamon, you can use 20:1 or even 50:1 FC. Warming the blade with a hair dryer can help.
More elaborate types of finishing methods and materials will give different results, and sometimes it requires some trial and error to pick which style to do. There are two main types of finishing ,which are chosen depending on how the hamon is formed and how it polishes - Hadori and Shashikomi. A simple way to differentiate which is which is to think of Hadori as "hardori" polish technique, and shashikomi as "softshikomi" polish technique. There isn't enough room in a simple post like this to explain the difference in more detail, and it is mostly a mater of experience and looking at the results to decide which to use. Usually you try hadori, and if the results don't work,try shashikomi.
Here are some final polishing (shiagi togi) abrasive/polish choices:
Wet-or-dry paper used with oil (Olive oil or choji oil work well). Start with 1000 grit, and work up to 8000 grit. Cut it into 1/2" squares ( keep them in a labeled zip-lok bag). This is sort of a poor-mans hazuya/jizuya stone.
Traditional Ha-zuya and Ji-zuya finger stones used with just enough water and polishing paste ( nugui).
Flitz - works surprisingly well, and leaves a shiny, but darker surface. Excellent for the ji. You can often use Flitz as nugui with ji-zuya stones.
Red Rouge ( iron oxide) in oil - deep dark luster. Use with a 22 caliber gun cleaning patch and your fingertip.
Chrome oxide powder in oil - usually brighter that rouge. Use as above.
Finely powdered magnetite in oil ( jitekou) - Use as above. Leaves a frostier surface equivalent to 1000-2000 grit.
Usually you have to polish above and below the hamon with different materials to get the detail to show.
Try making the ha bright by polishing with hazuya ( or other shiny method) right up to the hamon, and the ji darker with Flitz or rouge.
A trick for getting this effect is to polish the blade to 8000, and then go back and polish just the hamon with about 1000-2000 grit paper ( or jitekou) and then paint over the hamon with red fingernail polish or model enamel. Try and get the hamon covered exactly, including any wisps, with the polish. Then polish the ha with chrome/oil and the ji with Flitz or rouge/oil. Go right up to the enamel barrier. After the two surfaces are done, the top should be darker and the edge shiny. If that looks good, remove the nail polish with acetone, and use just a touch of Flitz or rouge/oil to blend in any harshness. Done right, this will leave a frosty hamon, a shining ha, and a darker ji. On some fake hamon swords, the same basic procedure is done, but there is no hamon there....just the frosted surface.
Some Google search targets for study:
Shitagi togi
Shiagi togi
Hybrid sword polish
Hadori
Sashikomi
Hadori vs sashikomi
Jitekou
