There are a variety of options. Arguably the best one if your project lends itself to it, is…pouring a final thin layer of clear epoxy onto the piece. It’s like magic, the original machined surface won’t show and you end up with a clear shiny finish. But of course, many times you can’t do this (e.g. if you would like to keep the wood surface alone)
What I often do is sand it manually, from 320 down to 3000 grit or so. But I’m really no expert, and I seem to remember folks mentioning a number of good tips, let me search…
EDIT: found the thread. You should ask @MikeG, @AndyC, and @fenrus, since they obviously get great epoxy finish.