I only use a semi colon to join two sentences that are related. I usually use a colon when a sentence ends with a list of three or more things and before an example or illustration. I wanted to look it up to confirm that I was correct; my instances are fairly correct but there are also more. The source I found doesn’t mention illustrations but I think they fit into the example rule.
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Colon.
A colon marks a pause for explanation, expansion, enumeration, or elaboration. Use a colon to introduce a list: thing one, thing two, and thing three. Use it to pause and explain: this sentence makes the point. Use it to give an example: this, for instance.
There are other uses: the entry on Citation includes some tips on colons in bibliographies. Americans use it after the salutation in a formal letter: "Dear Sir:" (the British use a comma, which we Americans restrict to less formal letters). It also introduces a block quotation or a list of bullet points.
Semicolon.
Semicolons probably produce more confusion and misery than all the other punctuation marks combined. But they're really not very difficult to master.
The semicolon has only two common uses. The first is to separate the items in a list, often after a colon, especially when the listed items contain commas: "The following books will be covered on the midterm: the Odyssey, through book 12; Ovid's Metamorphoses, except for the passages on last week's quiz; and the selections from Chaucer." The semicolon makes it clear that there are three items, whereas using commas to separate them could produce confusion.
The other legitimate use of a semicolon is to separate two independent clauses in one sentence: "Shakespeare's comedies seem natural; his tragedies seem forced." Here's how to tell whether this one is appropriate: if you can use a period and begin a new sentence, you can use a semicolon. In other words, this kind of semicolon can always be replaced by a period and a capital letter. In the example, "Shakespeare's comedies seem natural. His tragedies seem forced" is correct, so a semicolon can be used. (If you used a comma here — "Shakespeare's comedies seem natural, his tragedies seem forced" — you'd be committing the sin of comma splice.)
It's risky to use semicolons anywhere else. There's no need for them after, for instance, "Dear Sir" in a letter (where a comma or a colon is preferred). Don't use them before a relative pronoun ("She sold more than 400 CDs; which was better than she hoped") — it should be a comma, since the bit after the semicolon can't stand on its own. [Entry revised 10 December 2006.]
http://andromeda.rutgers.edu/~jlynch/Writing/s.html#semicolon
