Option 1:
Take LA Metro 460 Bus From
Disneyland To 7th Street Metro Center Station in Downtown LA.
Take LA Metro Redline or Purple Line Subway to Union Station from 7th Street Metro Center Station.
Then Take LA Metro Bus 733 or 33 from Union Station to Santa Monica Pier.
estimated cost: $5.25 per person, each way.
Option 2.
Get to either Anaheim or Fullerton Amtrak/Metrolink stations
Take Metrolink Orange County or 91 (Fullerton only) lines to LA Union Station.
Then Take LA Metro Bus 733 or 33 from Union Station to Santa Monica Pier.
tip: if you go this route, since you are traveling on a Weekend, you will be able to purchase a Metrolink Weekend Day Pass at $10. This pass is valid all day on all Metrolink trains an most connecting bus, subway, and light rail lines in the LA and Orange County area, including the 733 and 33.
estimated cost: $10.00 per person
Option 3.
Get to either Anaheim or Fullerton Amtrak/Metrolink stations
Take Amtrak train to LA Union Station.
Then Take LA Metro Bus 733 or 33 from Union Station to Santa Monica Pier.
estimated cost: $30.00 per person round trip
Links:
LA Metro:
http://www.metro.net/riding/maps/
Metrolnk:
http://metrolinktrains.com/
Amtrak:
http://www.amtrak.com/home