A is the definite article, and the is the indefinite article, so use 'the' when you are referring to a specific item (ie the left hand of my brother) and 'a' when you are referring to a non-specific or generic item (ie he learnt to ride a horse). 'An' is used when 'a' should be used, but the following word begins with a vowel (ie it is a fish and it is an eel).