In spoken English, the most noticeable difference are: The quality of vowel sounds, especially 'a' and 'o'. The letter 'r', which is pronounced quite strongly in most American accents and is pronounced in all positions in words. It is a much lighter sound in most British accents, and isn't pronounced after vowels (apart from in Scottish accents). The 't' sound between vowels, which is often 'flapped' in US English, so that it sounds a little like a 'd' sound In general, there's a more fluid 'rolling' sound to US English, compared with the more clipped sound of most British accents. In written English, there are a few spelling differences, for example: color/humor/favor (US) colour, humour, favour (GB) center/fiber (US) centre, fiber (GB) organize, analyze (US) organise, analyse (GB) traveling, fueling (US) travelling, fuelling (GB) There are also various differences in vocabulary (less than 5% of the total vocabulary) . The grammar is virtually identical. All of these are minor points. The main thing is that GB English and US English is the SAME language. It really doesn't matter whether you write 'centre' or 'center'. It doesn't matter whether you say 'film' or 'movie' - we will still understand you, and native speakers always understand each other. Regional differences in English are not the same as regional differences in Arabic. There is only one English, with a few unimportant variations.

Just to reinforce SuKi's answer, the difference is very, very small and becoming smaller every day. As a student, you shouldn't worry at all about which one you study. When you are very, very advanced and nearly fluent, you can start to consider the few idioms and other usages that are different. Just to give one example of the tiny difference: In the US, we call a small clip with serrations or "teeth" an "alligator clip". In the UK, this is called a "crocodile clip". Since the actual animals, alligators and crocodiles, look almost the same, there would be no confusion at all among native speakers.

This is something you can look up quite easily: http://en.wikipedia.org/wiki/Comparison_of_American_and_British_English