Use a semicolon to join two independent clauses* where a full stop would be too strong and a comma too weak:
1. The ferry was overloaded; the owners were clearly liable.
2. My sister loves mussels; her husband hates them.

Use a colon where what follows elaborates on what precedes it:
1. You'll never believe my luck: I'm going to Mexico.
2. You should have followed my father's maxim: 'Never borrow money'.

* An independent clause, or main clause, must contain a subject and a predicate: The ferry [subject] was overloaded [predicate] ... You [subject] should have followed my father's maxim [predicate]