There are many things to understand about fractions, but this page focuses upon basic numeracy.
The following Youtube videos give examples of these methods.
Adding, subtracting, multiplying and dividing - with simple fractions*
Adding, subtracting, multiplying and dividing - with mixed numbers
Multiplying with fractions - how to make them even easier
*The auto-focus on my camera decided to play a little havoc over the first 30 seconds or so of this video, but it does settle down - please be patient.