Probably the major differences between British and American English lies in the choice of vocabulary. Some words mean different things in the two varieties for example:
Mean: (American English - angry, bad humored, British English - not generous, tight fisted)
Rubber: (American English - condom, British English - tool used to erase pencil markings)
There are many more examples (too many for me to list here). If there is a difference in usage, your dictionary will note the different meanings in its definition of the term. Many vocabulary items are also used in one form and not in the other. One of the best examples of this is the terminology used for automobiles.
American English - hood
British English - bonnet
American English - trunk
British English - boot
American English - truck
British English - lorry
Once again, your dictionary should list whether the term is used in British English or American English.