Use a colon

before a list, summary or quote

1) Before a list.
I could only find three of the ingredients: sugar, flour and coconut.

2) Before a summary.
To summarise: we found the camp, set up our tent and then the bears attacked.

3) Before a quote.
As Jane Austen wrote: it is a truth universally acknowledged, that a single man in possession of a good fortune, must be in want of a wife.

to complete a statement of fact

Where the colon is used in place of the following or thus.
There are only three kinds of people: the good, the bad and the ugly.

Use a semi-colon

to link two separate sentences that are closely related

The children came home today; they had been away for a week.

in a list that already contains commas

Star Trek, created by Gene Roddenberry; Babylon 5, by JMS; Buffy, by Joss Whedon; and Farscape, from the Henson Company.