A very simple way to clean it is to use a bucket of warm water (not scalding hot and stay away from detergents) and let it soak for about 20 minutes, this should be enough to release any grime that builds up or gets spilled on it. Then hang it out to dry for a day or two (depending on weather). We would don't recommend machine washing and definitely don't use a dryer. If that's not enough to clean it then there are a couple products on the market that are intended to clean wetsuits (like you'd use to surf or scuba dive) which should be okay to use, but I would test in a small inconspicuous area before dunking the entire thing in a solution of it.
If you are concerned about building up yeast/mold on the outside of the neoprene (say you had a spill while you were pitching) and don't want to remove the neoprene right away, you can spray sanitizer or a neutral grain spirit (like a clear unflavored vodka or rum) on the jacket until you get the tank empty and can clean it in the manner above.