What's the difference?
If you have mainly been a student of American English, then it is possible that you have not come across the word 'shall'. Yes, this form is more popularly used in British English.
First, we do use will in British English - don't worry about that - and we do use it to talk about things planned in the future or to make a decision at the time of speaking. But the word shall is often used for the same meaning.
The word shall is, according to the Collins Cobuild Dictionary, often used in questions in order to make offers or suggestions, or to ask for advice, and is used with 'I' and 'we', for example: Shall we dance? Shall I call him now? What shall we do now? It is, in fact, a modal verb (remember them? see Not4GrammarBores for more information), and its past form is should.
Shall is, surprisingly, used in many other ways. It's used to referring to something that you intend to do, or sure will happen to you in the future: I shall give him 24 hours to make a decision. Also in speech or writing to say what you are planning: Later, I shall describe the effects. As we shall see, the Mona Lisa is quite a small painting. It is also used to say that something must happen: We shall decide on what's best for the company.
However, in most of these examples, will would be more commonly used, particularly in American English.
One example often given to express what difference does exist is in this. If you use 'shall' with 'you' when telling someone they can do something, or expressing a promise, you can say: You shall go to the dance! (Although, in reality, this is not often used as it sounds a bit old-fashioned!). Now, following this piece of advice, the phrase I shall drown and nobody will save me would state a clear fact. But them if we say I will drown and nobody shall save me, this suggests the speaker wants to drown even if help is available.
Although we use this modal verb regularly, it's one of those words which we don't worry over. Indeed, most writers don't worry about it much and most often use 'will'.