Colons and Semicolons
Colons and semicolons. Those two little vertical double marks. How do you use them? Well, fear not, for I am here to tell you. Both are used to connect related thoughts without the use of commas or a period, but they are used somewhat differently.
Colons have a number of different uses. They can introduce lists. Example: "I have three goals: to get rich, get married, and get famous." They are used (in America, at least) to format times of the day such as 12:00. Ditto for ratios (2:1). Colons are also used to indicate Bible verses such as Exodus 1:1.
Colons can be used to underscore an important point you're trying to make. Example: "This is the key to your success: hard work."
Should you capitalize after a colon? The answer will partly depend on which style you are using. Book Style is different than News Style. However, both agree that if the part after the colon cannot stand on its own, it's lowercase. However, Book Style says that if the words introduced by the colon make a complete sentence, the post-colon words should be lowercase. Example: "They made it very clear: you need to save your money." But News Style says that same sentence should have the "you" capitalized.
Now, let's talk about semicolons. They connect independent clauses that go together, and they separate items in lists where commas would be insufficient. Example for the latter: "He had two peaches which he received in Dallas, Texas; three apples, which he received in New Orleans, Louisiana; and four potatoes, which he loved."
Look out for the following words that may follow a conjunctive adverb: "however," "indeed," "therefore," "besides," "thus," "hence," or "besides." Those will all require a semicolon after them. Example: "He had a bad feeling about it; indeed, his fears came true."
The words "that is," "namely," "for example," and other similar words can be used immediately following a semicolon if they connect clauses that are closely related. Example: "He had some annoying friends; namely, Bill and Ted."
There are more rules for colons and semicolons, but I think this is a good start. For a complete list, read The Best Punctuation Book, Period. by June Casagrande. It's an invaluable resource for writers.