I’ve not spoke much before about teaching English abroad, but I have taught English in a few countries and the subject of American and British English comes up quite often, especially if I (as primarily British English instructor) come across students who have only been learning American English. I don’t think it’s a very advanced topic which should be left until they already have a good grasp of one of the styles as the differences aren’t that much or even that important, so it’s good to get them out the way early or even do a simple 1 hour lesson on the difference.
Of course if the students are learning English in Britain/Australia or English in USA, then it should be taught as per the local country. But if they are in their home country students should be taught to their (or the school) preference (not the teachers). If you refuse to do this (it’s certainly difficult to use a different version of English if you’re not used to it), then it would be more decent to find a student who wishes to learn your own than mis-teach the current student. Teaching English is one of the most common ways for travellers and expats to make some money to continue their travels living abroad so it’s good to know how to deal with this issue which I’ll cover here.
Accents are an advanced topic and not something most students can mimic until their English is conversational at least. Even native speakers struggle to put on some accents correctly. It is not something worth focusing on, but if you can show the difference, either with your own demonstration or a video then that’s probably best. Students will eventually pick out the difference between countries, but it’s not worth focusing on unless they specifically want to learn for business reasons as an example. Bearing in mind that their are easily over a thousand if you really want to break them down, and dozens you can probably think of by your own it’s not something that students need to learn. This isn’t even taking into account other countries like Australia, Ireland, South Africa, etc.
This in contrast is one of the most obvious ways of showing the differences. Words ending in ise (British) or ize (American). Something that can frustrate or humour (should that be humor?) students as well as native speakers. American tends to be the more simple and spelt like it’s pronounced. The lack of u’s in American is also another thing to point out. The best way to teach differences is plenty of examples which can be obtained from text books or other online sources.
Al-u-min-e-um or a-loom-e-num has caused a lot of humour at both sides of the pond laughing at one another. It also causes a lot of headaches for students that in my opinion should be familiarised with the differences. Many native people from both sides of the language get confused too. Ask for war-ter in a gas station (petrol station ;)) in the southern states and you’ll get a blank look half the time, it’s waa-ter there. As for Scottish, well I don’t even know where to start, och aye the noo maybe? I’d suggest dealing with specific regional colloquials as and when they come, you’ll be surprised by how much you know already just being a native English speaker.
All the Specific bits
I am only one person and covering specific language differences I feel is best done by a trained expert of a collaboration of efforts from both sides of the pond. This has already been done on a Wikipedia page which has far more detail than I could go into, so its well worth a look if you have a more demanding student who wishes to learn the differences.