To find out where to stay, just do a search for "rv parks" at google. Even better is google maps, try "rv parks las vegas". Many state and national parks have rv parks near or on site.
Many highways have RV park signs on the roads to direct as well.
Cost varies and can be paid by the day, week, month or longer. Rates include power, sewage and water hookup and usually wifi. Some walmart stores offer free parking overnight, but check with the store manager before hand. Otherwise you may get woken up in the middle of the night by the local cops.
It's a great way to travel. You always have your shit with you and you always sleep in your own bed.
Just be careful and don't do this:
http://www.ebaumsworld.com/video/watch/743647/