updated May 31, 2023
Many people own second homes in Las Vegas (and elsewhere in Nevada; Lake Tahoe comes to mind). In Las Vegas, especially, it's often advantageous to be able to prove you're a resident, to get in on the good deals available only to locals, not visitors.
While it's not possible to get a Nevada driver's license without completely relinquishing the license from your home state, a "Seasonal Resident ID Card" is available that will, in most cases, enable you to obtain the same locals' discounts that those with a Nevada driver's license can get.
To qualify, you must indicate that you spend at least 31 consecutive days in Nevada each year, maintain a temporary residence in the state, aren't gainfully employed here, are registered to vote or pay income tax in another state, and return to the state of residence at least once during a calendar year (otherwise, you'll be considered a resident and will have to surrender your out-of-state ID).
To apply for the seasonal ID, you must appear at a Nevada DMV office with the following documents in tow: current driver's license (from whatever state) or proof of identity, two documents with proof of Nevada residency, one document to prove your Social Security number, and, if applicable, a marriage certificate to validate any post-marital name changes.
You fill out the regular Nevada driver's license application, except you check the box next to "Seasonal ID Card." Your picture is taken and your card is mailed to your Las Vegas address in two weeks.
The Seasonal ID Card must be renewed every 4 years. Note that the ID card actually expires on your birthday short of four years the first time you renew; if you miss the renewal date, you must start the process all over again, so watch your mail carefully.