Take the train to Bayeux (from Paris? you didn't say). If from Paris it's a bit over 2 hours, but add the time to get to the station, wait for train, etc.
Then get from the Bayeux train station to the Bayeux bus station (don't know how to do that, you could go to viamichelin.com and figure it out).
Here's the Normandy bus route map
http://www.busverts.fr/_hiver/plan.asp
Note that I have not done this by bus. But I'm going to go ahead and describe what I think might be a way to get from Bayeux to the American Cemetery. I said "think", this is theory. If anyone here has actually done it, please help us out.
Okay, back to the bus map. You're at the Bayeux bus station. (BTW, bus website is in French, no English version).
Click on the upper left of the map, so that you get a larger version that shows Bayeux and area northwest of Bayeux.
Look for the green route on the map, it says #70. You can see it goes northwest from Bayeux. One of the stops on the #70 route is Colleville. The American Cemetery is about 1.25 miles by road north of the center of the town/village of Colleville-sur-Mer, I assume the Colleville stop on the bus map lets you off in the town of Colleville-sur-Mer.
If you go by bus, I guess you have to walk the last 1 and 1/4 mile.
Which raises the subject of taxi (see post below).
