If you don't have a buffing wheel (or wheels), buffing compounds, and a good cleaning rake for changing compounds, it'll take a while.
What worked for me was using a series of wet/dry sandpaper followed by hubcap polish (chose one that didn't require ventilation to use). Used 220, 400, 800, and 1,000 (because that was what was in the variety pack) and finished off with hubcap polish, a scrap of shop towel, and elbow-grease.
Start with a 220 or 320 grit piece of wet/dry and get a series of uniform scratches covering the entirety of what you're polishing. As wet/dry sandpaper looses its bite very quickly, use different pieces for each side.
If you switch between putting vertical and horizontal scratches on your blade as you change from grit to the next, it's easier to see when the previous grit's scratches are completely removed. If you're not comfortable with switching directions, you don't have to, but since scratches like to hide, you may need to redo you polish from 400 or 600 grit to wherever you choose to finish before using the polishing compound. That's okay; it's just more practice.
Once you're done with your final piece of wet/dry paper (please use 1,000 grit as your bare minimum and if you use 2,000 or 2,500 grit as your final piece, you're already done!), put a small amount of hubcap polish on a scrap of shop towel or even paper towel and carefully go back and forth across the surface you're polishing until the compound turns pitch black. Grab another scrap and repeat and grab another scrap and repeat and keep going until you're too tired. Wash off the blade, wipe it dry and wipe away any polish residue you missed while cleaning, and enjoy.
Do not do this while you're tired, while you're distracted, or after you've had an intoxicating substance (liquors drunken me) as part of that surface is an edge and it's been sharpened very keenly on wet/dry sandpaper and will love to taste a little finger or thumb.