Take the bus. There's a line that runs from the airport through downtown. Normally, it's about a 10 minute ride from the airport to Santa Fe station.
There's an airport stop for the Trolley. It is at the airport kinda. It's on the other side of the tarmac from where the terminal buildings are but there's a shuttle. It's the midtown stop. You should be able to walk it too. Often I thought about hoping off there and walking to the terminals before it became the official airport stop.