How should I properly use a semi-colon?

There are many different ways in which a semicolon can be used. 

The first, and the most common is to link two similar clauses together. For example, you could say, 'The lady had a cat. The cat was brown', but instead, you would use a semicolon to say 'the lady had a cat; it was brown'. This makes the sentence appear more sophisticated to examiners. 

Another way in which a semicolon can be used is to link lists where there are multiple commas to avoid confusion. For example: 'I need you to get: a camera, which can be found in the photography store; a new book, from the shop next to it; and a loaf of bread from the supermarket'.  In doing this, one item, and the directions for it are separated from the next item. 

Semicolons can also be used to link lengthy clauses to avoid confusion between them. You could say 'I like mangos, apples, and oranges, but, unlike my sister, I do not like grapes', which has several clauses and is therefore confusing. Instead, you could now say, 'I like mangos, apples, and oranges; but, unlike my sister, I do not like grapes'. 

There are other ways to use semicolons, but it is unlikely that they will be needed at GCSE level, or indeed in essay writing.