If you want to get anywhere fast that doesn't involve the light rail...you're pretty much out of luck. This is one of the fastest growing cities yet has the worst public transit system. Only reason I use the light rail/bus is because I can't drive yet and gas is expensive.
Bus: Expect broken A/C systems in the summertime, creepers after 8PM, and buses that show up an hour late even on weekdays (I'm thinking the McClintock Apache bus station Southbound right here). Oh and you may not even want to trust the posted bus schedules at their respective stops because they never arrive on time.
Light Rail: The light rail is decent although I wish for a city this big they had just gone ahead and done it back in the 60's when they had decent funding to do so from what I heard from an old-time valley native.
Sometimes you can get free rides: for buses if the fare box is broken; the light rail if no security is on board (usually early mornings, afternoons).