Semicolons and colons are great for adding variety to your sentences and establishing bonds where necessary. But they are often misused because of their fluidity. It's also easy to confuse the two. So let's take a look at each and clarify when they are appropriate.
Semicolons
Semicolons can be used to link two sentences or ideas that are closely related but function independently. The joined sentences will often have a cause/effect relationship and are considered to be of equal weight. In other words, they express a similar idea or outcome.
Example: I went to the store; we were out of laundry detergent.
In the example, using a period after "store" would also be correct. However, the second half of the sentence serves as a cause to the first half, so joining the two clauses makes sense.
A good test to use for semicolons is to replace the semicolon with so or because. If the sentence makes sense with one of those words, a semicolon is likely suitable. Of course, writing the two sentences separately with a period at the end of each is always acceptable. So, if you're not sure whether the clauses can be linked with a semicolon, use a period instead.
Semicolons can also be used to separate items in a list when the items are lengthy or when you have lists within the overall list.
Example 1: When writing a book, you should consider all the characters involved and how they interact with one another; the plot and any related subplots; and what the overall goal in telling the story is (i.e. whether the protagonist will succeed or fail in getting what they want).
Example 2: In order to bake the cake, we need to buy: red, white, and blue berries; white and chocolate cake mix; and tall, medium, and short candles.
A semicolon should never be used to join fragments or to connect two independent clauses with a coordinating conjunction (e.g. and, but, and or). A comma is the appropriate punctuation in those situations. The only except is when you have a list within a list, as illustrated in the previous example.
Lastly, semicolons are used to join two main clauses with a conjunctive adverb (e.g. however, therefore, and instead). These adverbs often show cause and effect, sequence, contrast, comparison, or other similar relationships. (See Wikipedia's entry on conjunctive adverbs.)
Colons
Colons are known as the drum roll punctuation. They are used to introduce or define something and to connect related ideas of a different weight.
Example 1: In our garden this year, we planted several things: lettuce, carrots, peas, tomatoes, and cabbage.
Example 2: You only need one thing: common sense.
A good test to for colons is to replace the colon with a comma and the word namely. If the sentence still makes sense, a colon is acceptable.
Unlike the semicolon, a colon can actually be used to join an independent clause with a fragment, usually a noun. It's important to remember though that the independent clause must precede the colon, not follow it.
Note that just as with periods, colons only require one space after them.
Capitalization after a colon is another common question. The short answer is, it depends on the content following it. If the clause following it is a fragment, you should not capitalize the first word. However, if the clause is independent, a stylistic choice must be made. My preference is to capitalize the first letter of the word following a colon, but the most important thing is to be consistent. Also, if there is a proper noun following the colon, such as a name, then the first letter of the following word must be capitalized.
Quick Overview of Semicolons and Colons
1. Semicolons are used to join two independent sentences that are closely related; for separating long items in lists or lists within lists; and to connect two main clauses using a conjunctive adverb.
2. Semicolons should never be used to join fragments.
3. Semicolons cannot replace colons.
4. Colons are used to define or introduce the content following it and can be used to join an independent clause to a fragment.
5. Only one space should be used after a colon.
6. The first word after a colon should not be capitalized if the clause is a fragment; otherwise, capitalizing the first word after a colon is optional unless a proper noun is used.