There are a ton of differences between British English and American English, but I thought I’d highlight some of the ones that stick out in my head that I notice that you may run into.
The biggest difference that I hear is the difference between 
vocabulary:
US/British
apartment/flat
trunk/boot
wrench/spanner
vest/waistcoat
jumper/sweater
diaper/nappy
Spelling differences:
US/British
gray/grey
theater/theatre (er is switched to re)
color/colour
favorite/favourite (0 is changed to ou in many words)
memorize/memorise (lots of words where the z and s are changed)
check/cheque (ck -> que)
Those are just a few of the differences that I come across often, to see more differences, refer to these websites:
http://en.wikipedia.org/wiki/American_and_British_English_differences
http://www.woodlands-junior.kent.sch.uk/customs/questions/americanbritish.html