By Air : The LAX Airport (LA International airport) is the closest to Santa Monica. It is well connected to domestic as well as international destinations. From the LAX you can go down Santa Monica by FlyAway® Bus service, or the Big Blue Bus or shuttles or pre booked taxis.
By Train : If you plan on going via rail, the Amtrak is the closest and is situated at Union Station, downtown LA.
HOW TO GET AROUND SANTA MONICA
The best way to explore Santa Monica city is by foot or bike! However, if you decide not to travel this way, you can always hop onto a Big Blue Bus. It is well connected and has around 1000 stops all across the west side of LA.
The Santa Monica Shuttle service was launched recently in May 2014. This service is however a hotel-sponsored service and hence you need to check up with your hotel help desk about it.