While there are certainly many more varieties of English, American and British English are the two varieties that are taught in most ESL/EFL programs. Generally, it is agreed that no one version is "correct" however, there are certainly preferences in use. The most important rule of thumb is to try to be consistent in your usage.
This fun tool "translates" British English to American English and vice versa. Finally, once you've understood all the differences (good luck!), you can try this American English vs. British English quiz.