Colons can be used to introduce lists and quotations.
We need to buy three things: milk, bread and butter.
My mum has a favourite saying: "Never worry about things that might not happen."
A colon should only be used in this way if the first part of the sentence makes sense on its own. In the following sentences, the underlined parts do not make sense on their own so a colon should not be used.
We need to buy milk, bread and butter.
My mum always says, "Never worry about things that might not happen."
You can also use a colon to emphasise a point.
Sid is particularly well known for his greed.
By rewriting this sentence with a colon, Sid's greed can be highlighted.
Sid is particularly well known for one thing: his greed.