Palm Springs has its own airport (PSP). There are direct flights from the east coast on Jetblue and Virgin America (beginning January 2016).
Flying to Los Angeles (LAX) and then hitting the road is also an option. But don’t hit it during AM or PM rush hours, as LA’s world famous traffic will turn what should be a two-hour drive into double that. If you don’t feel like renting a car to get to Palm Springs, a plethora of car services will be happy to drive you, and there are some shuttles (www.ampmshuttleservice.com, www.atyourserviceshuttle.com).
Another option that we have utilized is the John Wayne International Airport in Orange County (SNA), which is actually a slightly shorter and less traffic-riddled drive than from LAX. You can also fly into other SoCal airports such as Ontario (ONT) which is only an hour away, Burbank (BUR) and Long Beach (LGB) which are about the same distance as LAX, or even San Diego (SAN) which is about two and a half hours away.