By now, most people have gotten used to the changes in airplane travel instituted over the last decade (I have to take my shoes off? really?), but the basics are still worth mentioning to ensure you don't get delayed any more than you have to.
First, put everything that could even be thought of as sharp or liquid in your checked bags and only bring what you absolutely have to have with you in your carry-on. This includes everything from nail files to tweezers to those jars of eye cream you think you need to have with you so you can look fresh as soon as you hit the tarmac.
McCarran International Airport is one of the most modern and well-planned airports I've ever visited. As usual it can be a bit of a hike from the gate to the baggage claim or taxi line but for most terminals they have either motorized walkways or trains that will whisk you to your destination a little more quickly. All roads from your gate will lead you to baggage claim, which is remarkably faster than most major city airports that I have been to. Not fast, mind you, but faster. Read more about the airport here.
After you've grabbed your bags it is time to find your way to your hotel and this brings me to my most important bit of advice. I've said it before and I'll say it again... if you are planning on spending any significant amount of time in Vegas (more than 1 or 2 days) then you absolutely should rent a car. Yes, traffic in this city is a pain, but that's no different than in any other major city, and the advantages are legion.
If you're planning on doing any exploring of the city, you'll have a much easier time with a rental car and in the long run will probably save yourself some money over taking cabs everywhere. Parking, both self and valet, is free and plentiful at every major hotel and attraction that you'll want to visit. Read more about car rentals here.
But if you are dead set against renting a car, there are other ways to get around. Just outside the baggage claim area is where you can grab a cab or a shuttle bus to The Strip. Don't worry about calling in advance - they are always there, although at peak times there may be a line to get transportation. Unfortunately there's no way around that.
Cabs are also usually in plentiful supply no matter where you go - certainly at every hotel and near most off-Strip restaurants and major attractions. Hailing a cab here is easier than it is in New York City, land of a million cabs.
For getting around The Strip you have four options: drive yourself if you have a car, cab it, walk it, or take public transportation. We've already covered cars and cabs so let's talk about the other options.
The Las Vegas Monorail connects MGM Grand with The SLS Las Vegas and stops at Paris & Bally's, The Flamingo, Harrah's & The Quad, the Convention Center, and LVH: Las Vegas Hotel in between. It's convenient if you are going where it goes but not so much if your final destination is somewhere off the route. Read more about the monorail here.
Another public transportation option is to use the city bus service. The Deuce is a double-decker bus that trolls The Strip from Downtown Las Vegas all the way out to the Las Vegas Outlet mall, with stops at every major hotel along the way. Read more about city buses here.
Several off-Strip hotels also have shuttle buses that run to their properties. If you're interested in visiting a specific place, check their website or call to see if they have shuttle service.