Well, of course the easiest way for many folks to arrive in Palm Springs is through the Palm Springs International Airport (PSP) (yup -- international).  It's a small but beautiful airport with everything you could want.  Major carriers, and regional airlines bring flights in from other California airports as well as Seattle, Texas, Arizona, Canada and beyond. 

If you are flying but can't get into Palm Springs directly, then Ontario (ONT) and John Wayne Airports (aka Orange County/Santa Ana/SNA) are your next best bets.  You can also arrive via LAX, Long Beach (LGB), Bob Hope (aka Burbank/BUR) or San Diego Lindbergh Field (SAN).  All of these choices will require a rental car and a little bit of a drive, but not too bad if the airfare warrants.  

Palm Springs is right off of the I-10 Freeway for those driving into town.  

As part of the Amtrak California program that is mainly funded by CalTrans, there is a Thruway Bus to/from the Fullerton Train Station twice a day with a few stops.  More info can be found at Amtrak.com