These differences are important for teachers who are American teaching abroad. You will find British-isms sneaking into your vocabulary and writing after a while, and sometimes it may be difficult to remember which is which! It is especially important to distinguish between the two styles when clarifying differences for your students who need to take an exam in either American (ie, TOEFL) or British English (ie, LCCI).
This one is actually extremely annoying to my American ears, as I was taught that 'have got' is improper English. Actually, it is the spoken form of 'have' for many Brits, though the written form should be the American standard spoken and written form of 'have'. For non-native speakers, 'have got' is actually much more confusing, because it looks like a present perfect form of the verb and has a more confusing question pattern (Have you got a pet? vs Do you have a pet?). I recommend teaching 'Do you have/ I have' to Europeans, though an explanation of the British usage may be necessary depending on which book you use.
My general rule of thumb is to follow more French or softer spellings for British English:
recognise (Brit) recognize (Am)
theatre (Brit) theater (Am)
travelling (Brit) traveling (Am)
colour (Brit) color (Am)
practise (Brit) practice (Am)
dialogue (Brit) dialog (Am)
The above are the most common. You can find a more detailed list on Wikipedia.
There are many word differences that mostly end up being dialectical, depending on what part of England, Australia, Canada or America you come from. However, there are a few that you run into over and over in language books which are helpful to recognize right away:
ring (Brit) call (Am)
sort out (Brit) work out (Am)
book (Brit) reserve (Am)
queue up (Brit) line up (Am)
Generally, the Brits use a little less punctuation than Americans do in their letters. You do not need a comma after the greeting of a British letter, though I sometimes see it included after the closing. Also, titles do not need punctuation, such as Mr or Mrs, as they do in American English. Dates are written in the more European style, with the day before the month (24 June) instead of June 24th.
There are many more subtler differences between American and British English styles to consider, but this article should give you some basic differences to build from. Generally, for academics, the differences that are most important are found in writing style and spelling. Spoken differences are less important, as the intended meaning should be clear to both the American and British speaker, even if there are subtler differences between the two's speech patterns.