Making a beautiful cutting board by hand is surprisingly easy. All you need is some scrap wood, saw, and sander power. This took me a while to make because of my own inability to use a table saw, but with proper and correct saw use, it's as simple as one cut, sand and seal. It's great for parties and showing off a fine piece of your own handiwork to friends.
Step 1: Find Your Wood
Choose a cross section of wood that you can get your hands on from the local area.
I found: Redwood, Black Acacia, Various fruit woods, and Monterrey Cypress.
Check the wood out on Wood Database, looking in particular to Janka Hardness, allergens/toxicity, and workability.
You're looking for higher Janka Hardness, so you don't cut into the board, little to no known reactions/toxins to avoid handling food on it, and decent workability so aplitting doesn't become an issue.
I chose Black Acacia because it looks great, Janka of 7590 Newtons, and seems like a cool wood to experiment with.
Step 2: Cut Your Board
Using a table saw, or saw, or axe for pros, cut the board perpendicular to the grain. Approximate the shape you will want (handle/no handle) and cut a bit large for sanding.
Step 3: Fill Holes and Cracks (optional)
This step isn't required, but can add performance if your cutting board is cracking. I'd recommend properly drying your wood before working with it.
Step 4: Sanding
Sand that board. I have no power sanders so this became a laborious task. If only I was sanding redwood at this point. I made the mistake of having the board larger than my table saw, and didn't cut it perfect, so I took the mistake and went with it, using a chisel to make this pattern along the elevation change.
Step 5: Clean and Seal
Oiling and cleaning your cutting board is key to keeping it in good condition for the years to come. I prefer and oil based seal over plastics, as plastic can wear into food while cutting.
Step 6: Enjoy!
Show off to your friends, yourself, or your dog that you ditched that plastic cutting board.