To be honest we're not the biggest fans of colons and semicolons – as long as it doesn't change the meaning we'd rather you use dashes or rewrite the sentence.
But if you can't fend them off, follow these rules on how to handle them.
Use a colon to introduce something that follows logically from and depends on the preceding text:
This includes reported speech:
Use a semicolon to link two related parts of a sentence, neither of which depends logically on the other and each of which could be single sentences:
You can also use semicolons in a complicated list or sentence if it will make it easier to read, particularly if some of the listed items already include commas: