There are a number of differences in the way that the British and the Americans spell words. Some of the main differences are listed here (AE = American English; BE = British English):
1. -re or -er
A lot of British words that end -re have the ending -er in American English, eg sombre (BE) - somber (AE); litre (BE) - liter (AE). This is most common for words ending -bre or -tre. Words ending -cre (eg acre) are not changed in AE.
2.-our or -or
The British word ending -our is usually changed to -or in American, eg odour (BE) - odor (AE)
3a. -ise or -ize
The Americans generally use -ize, whereas the British mostly use -ise (although -ize is also used in Britain for some words) eg organise (BE) - organize (AE and BE); realise (BE) - realize (AE and BE).
3b. -yse or -yze
The Americans use -yze, whereas the British use -yse, eg analyze (AE) - analyse (BE)
(For information- although the "ize" ending is at present the preferred usage in the US and the "ise" in Britain, in fact "ize" was the preferred spelling in past centuries. Some British dictionaries encourage the use of -ize, so it could be that the preferred usages change in the future.)
4. -ogue or -og
The British use -ogue, whereas the Americans generally use -og. Eg monologue (BE) - monolog (AE). (Note: the ending -ogue can also be used in American English.)
5. -ce or -se
6. Double 'l'
a) In British English, for many words ending in a single 'l', this 'l' is doubled when adding endings such as -ed, -ing, -er, -est, -er, -or. In American English the 'l' remains single. Eg cancel, counsel, cruel, dial, equal, fuel, grovel, label, level, marvel, model, quarrel, travel.
b) There are some words where the Americans use double 'l' where the British use one (although not in all forms of the word), for example: