To clean the board: wash with warm, soapy water and dry immediately. We find a chef's bench scraper is a great way to gather up the crumbs on a big board that we don't want to lug to the sink. You don’t need to worry about it too much, but in general don’t give it too much water exposure. Don’t leave it sitting in a puddle, or even on a damp towel. Prop it up so that air can flow evenly to both sides between uses.
Uneven exposure to moisture — such as leaving it sitting on a damp towel, or trapping moisture under it — will cause the board to warp. You might wake up in the morning to find you’ve got a bowl instead of a board, but don’t worry! When the moisture evens out it’ll return to flat. Lean it so that air can flow to both sides and wait a day or two.
You should refresh the finish occasionally — every week or few weeks or month, depending on use. My Beespit cutting board polish works great if you want to bring back the original shine. You can use some cooking oils, especially nut oils such as walnut, although avoid vegetable oils that will go rancid over time. The cheapest bet is to pick up a bottle of mineral oil from the drugstore: it’s cheap, odorless, colorless, and works just as well as anything else. It's especially useful as a primer before putting on Beespit polish (and that's what we do here in the shop).
You can also lightly sand your cutting board to restore the fine polish on the surface, if you like. It’s solid wood and it’s yours — sand it all you want. Personally, I prefer the character that all the slicing and chopping gives it. Your cutting board is a tool, after all — a very beautiful, lovingly crafted tool. Enjoy it!