Prior to my recent introduction to Uber, this was my number one mode of transportation to and from McCarran. It's non-stop from the Golden Nugget downtown to the airport and will set you back $9.00. Beats the heck out of troubling someone for a ride or paying to park at McCarran.
The shuttle operates around the clock, but make sure you call ahead and make a reservation, as they won't just roll by. It's my understanding they will only pick up if someone is scheduled. You can just hop on when they show up, but if nobody has scheduled a pick-up, you may be standing around for awhile. Speaking from experience here:-)
From McCarran, they run about every thirty minutes and service the famous LV Strip and all downtown hotels. It's definitely a relatively convenient and inexpensive way to get yourself to and from the airport. Safe travels