Flight
LAX is the biggest nearby airport. Located about 90 minutes away, you can rent a car and drive up to Santa Barbara or reserve a seat on the Santa Barbara Airbus which shuttles you from LAX to SB multiple times a day for a reasonable price.
Rental Car
With multiple buses to and from SB to LAX daily, the SB Airbus is the best of option for those unwilling to rent a car and drive to SB.
Flight
You can book flights out of Santa Barbara but they tend to be a little more expensive and add an extra layover somewhere in the middle of the US. But it's definitely convenient!
Rental Car
The drive from LAX to Santa Barbara is pretty straight forward. California does not have great public transport so this is your best option for getting to and around Santa Barbara.