Ask when you make your reservation what transportation is offered free by the hotel. Many of the Strip hotels offer free shuttles to the airport, to shopping malls and to other Strip hotels. Hop aboard the Strip trolley. The trolley goes up and down the Strip with stops at all the major hotels. The Strip in its entirety is four miles long, so you may want to stick to the area around your hotel.
Buses run to all areas of the city, with three lines serving the Strip.
Take a monorail. Some hotels have monorails that connect them with other hotels - for example, you can go from Bellagio to the Monte Carlo or from Excalibur to the Luxor and Mandalay Bay. This service is free. Most casinos and Strip hotels have huge parking lots. You can choose between valet and self-parking.