You should use a semicolon in the following situations:

1. To connect two closely related independent clauses (complete sentences) that are not joined by a coordinating conjunction (and, but, or, nor, for, so, yet).
   Example: "I do not like to eat chocolate; ice cream is my food of choice."

2. To connect two independent clauses that are linked by a transitional word or phrase such as however, therefore, for example, in addition. The semicolon comes before the transitional word, which is usually followed by a comma.
   Example: "I do not like to ride the bus; however, I ride it when I visit my sister."

3. To separate items in a series or list when the items themselves contain commas or internal punctuation, to avoid confusion.
   Example: "Classic science fiction sagas are Star Trek with Mr. Spock and his large pointed ears; Battlestar Galactica with its Cylon Raiders; and Star Wars with Han Solo, Luke Skywalker, and Darth Vader."

In summary, semicolons are used to link related but independent sentences more closely than a period would, and to clarify complex lists where commas alone would be confusing. They create a pause stronger than a comma but softer than a period, showing a clear connection between clauses or list items.