Colons serve primarily two purposes. The first is to precede a list of three or more things in a sentence, and the second is to join two clauses of a sentence. For the first purpose, however, you should avoid using a colon after a verb or a preposition. The best way to correct the sentence above is to delete the colon. 

Colons serve primarily two purposes. The first is to precede a list of three or more things in a sentence, and the second is to join two clauses of a sentence. For the second purpose, however, you may only use a colon where a period might otherwise be used. The best way to correct the underlined portion above is: "I abhor the way totalitarian states treat their citizens: their behavior towards thier own people is simply inexcuseable."

Colons serve primarily two purposes. The first is to precede a list of three or more things in a sentence, and the second is to join two clauses of a sentence. The colon is missing prior to the list above, the best way to correct the underlined portion is: "here: we"

Colons serve primarily two purposes. The first is to precede a list of three or more things in a sentence, and the second is to join two clauses of a sentence. For the second purpose, however, you may only use a colon where a period might otherwise be used (after an independent clause).

Colons serve primarily two purposes. The first is to precede a list of three or more things in a sentence, and the second is to join two clauses of a sentence. For the second purpose, however, you may only use a colon where a period might otherwise be used. The best way to correct the sentence above is to delete the colon. 

Colons serve primarily two purposes. The first is to precede a list of three or more things in a sentence, and the second is to join two clauses of a sentence. For the first purpose, however, you should avoid using a colon after a verb or a preposition. The best way to correct the sentence above is to delete the colon. 

Colons serve primarily two purposes. The first is to precede a list of three or more things in a sentence, and the second is to join two clauses of a sentence. For the second purpose, however, you may only use a colon where a period might otherwise be used, after an independent clause, and for this use of the colon the second clause should explain or define the main clause. In this case, the dependent clause directly explains the main clause, so the best way to correct the underlined portion above is, "The truth of the matter is, as always, rather simple"

The example sentence includes a list of three items. Often lists of three or more items are preceded by a colon (unless the last word before the list is a verb), but they should not be preceded by a semicolon. Semicolons are used to combine independent clauses into one sentence. Since the second clause is nowhere near to a grammatically complete independent clause, we know that a semicolon will not be the appropriate form of punctuation. The correct version of the example sentence reads, "I ate four terrible things yesterday: a raw squash, a cold turkey sandwich, and a hot popsicle."

You are only permitted to use a colon to separate clauses (one of the clauses may be a list) when the colon is placed where a period could also logically be placed. In the sentence above, the colon is incorrect because you can't put a period after "My three favorite games are." The best solution is to eliminate the colon altogether. Note that because the items in this list are proper nouns it is correct to capitalize them.

Colons serve primarily two purposes. The first is to precede a list of three or more things in a sentence, and the second is to join two clauses of a sentence where the second clause explains, defines, or clarifies the first. For the second purpose, however, you may only use a colon where a period might otherwise be used. In the example sentence a colon would correctly follow the first independent main clause, and would make clear the relationship between the two independent clauses.

Note also that coordinating conjunctions should not follow colons being used to connect two independent clauses, just as coordinating conjunctions should not follow semicolons.