$20 is not a bad rule of thumb, especially if the service is good. Another guideline (for the US), which also works for restaurants where you're given free dishes, complementary spa services, and other situations where you're receiving a free service but tipping the service provider is appropriate, is to tip as if you were paying the normal price. If you don't know the normal price, you can use your best estimate.
So what does a limo ride from LAS to a strip hotel normally cost an average customer? The first few Google results indicate a range of $90-$150 round-trip depending on the size of the car. So that's roughly $45-$75, giving a rough tip range of $10-$15. Since you're not paying for the ride, bringing that up to $20 would be a nice thing to do.
As far as physically giving a tip, you can't really go wrong. A typical thing to do (outside of restaurants, where you don't hand money directly to the waiter) is to fold up the bill a few times, roughly like this, place it sticking out of the palm of your hand, and pass it to the driver while thanking him. No need to say "I'm giving you a tip now" or anything like that. If you were paying him for the service as well, you could just give him more money than the total and say "keep the change," or ask for a specific amount of change back (e.g. "Can I get 5 back please?", which they will understand to mean the rest is a tip).