The colon is the most abrupt piece of punctuation; it brings the reader to a screeching stop. Picture it as two periods, stacked. As such, it must always be preceded by an independent clause (i.e., a complete sentence), which would require a period if it were to stand on its own. The colon may be followed by a phrase, a list, a quotation, or even another independent clause.
✓ Remember what the road sign said: Don’t Drink and Drive.
✓ When Jacques Villeneuve was a young boy, he had one dream: he wanted to be a race car driver.
The semicolon is the most misused and misunderstood piece of punctuation. Essentially, semicolons exist only to join independent clauses (i.e., complete sentences). Picture it as a period sitting on top of a comma. The period signals that the semicolon must be preceded by an independent clause; the comma indicates that the semicolon intends to link related elements into a single sentence. Do not use a semicolon between unequal parts of a sentence, such as between independent and subordinate clauses, where a comma is called for.
✘ Han Solo advises R2-D2 to let Chewbacca win their chess game; because Wookies are sore, and dangerous, losers.