There is no "today's price". It's a futures market. "CL" means Crude Oil, "H" means March, and "10" means 2010.
So CL.H10 means March 2010 delivery. Because it's a finite commodity with a specific delivery date, it's not traded like a stock, and there's no symbol per se.
When you hear the price of oil quoted on TV, they're quoting the price of oil that is to be delivered next month - which in this case is CL.H10.
http://quotes.ino.com/exchanges/?r=NYMEX_CL