There's practically no steps to this. I feel almost silly even writing it, but there's some small knowledge here that can make a big difference if you make one, and that's why I'm gonna be talking about it. The key is in the sanding.
First of all, why the hell didn't I have a cheeseboard until now? I love cheese! I've been cutting the stuff on plates and that's just dumb. I've broken plates this way and certainly dulled my knives. The best thing to cut on while look like a classy son-of-a-gun in the process is definitely real wood.
I'm using Walnut because it's super sexy, but also is really good to work with and will give a great finish. Step one is obviously to just cut your board. I'm gonna use a live edge because I have access to great pieces of wood, but you can make a fancy shape, leave it square, or anything really. Whatever your shape, I say simpler the better, because the faster you're done, the quicker you can load it up with cheese and meats.
After the shape is established, it's time for the un-fun and necessary... lots of sanding. Don't skimp on this part, and don't think you can get away with one grit and make it nice. You really have to step down with the grit, and this will make not only a better product, but it'll go faster too. If your board is relatively smooth from a planer, then start with about a 80 grit on an orbital sander. After you have sufficiently smoothed out any major imperfections, it's time to change the grit. Next hit it with some 120, then 220, then 320, and if you're really going for that silky feel – 400 with a hand block sanding in the direction of the grain. At this point, the bare wood will be so smooth you won't want to stop touching it.
Next blow the dust off with a compressor or use a tack cloth to get the dust off. If you're sanding furniture, I like a little dust in my finish to fill the grain... But we're going to oil this piece to make if food safe, and I don't want any dust in my cheese.
Apply some mineral oil to the wood with a soft cloth and then remove any excess with another cloth. You can apply a few coats, making sure it soaks into the wood plenty. After a cure period of a couple days, you're ready to use it. You can reapply oil every once-in-a-while to keep it looking good... and if you're doing tons of cutting, you can always re-sand to get it back to the original condition.