Rule 1: Connecting Independent Clauses
Use a semicolon to connect closely related sentences or independent clauses linked with a transition word or phrase.
 
Example: I went to the store; I was out of milk.
The second sentence clarifies the first; therefore, a semicolon is used.
 
Example: The second sentence clarifies the first; therefore, a semicolon is used.
"Therefore" is a transition word, and the two sentences relate. 
 
Examples of transition words are as follows:
Therefore     However     Nevertheless    Thus    Finally    Likewise
Moreover     Consequently     Instead    Still    Then    Otherwise

Examples of transition phrases are as follows:
On the contrary      As a result     On the other hand
In other words     For example     In fact

Rule 2: Separating items in a list filled with internal punctuation
 
Example: Dianne, the maid; Theodore, the butler; Anastasia, the nanny; Richard, the cook; and Reginald, the chauffeur are the characters accused of murder in a detective novel.
 
Because of the commas separating the appositives from their nouns, semicolons are used to keep the sentence clear.
 
Exercise
1. I went to the store; and it was crowded.

store; it correct

2. Paul and Erin are engaged therefore, they came together.

engaged; therefore, correct

3. Mr. Smith goes to Washington every year; because in Washington there is great apple picking.

year because correct

4. Sparkles, the dog; Pickles, the cat; Bubbles, the fish; Scaly, the iguana; Rick, the snake; and Percival, the donkey, made the trip with Rebecca to San Diego.

snake, and correct

5. I felt, therefore, that I had a right to the property.

felt; therefore, correct
 
Answers
1. store; it (no need for the conjunction with a semicolon)
2. engaged; therefore, (without the semicolons, the sentence is a run-on)
3. year because (the clause following "because" is dependent)
4. correct
5. correct (the clause following "that" is dependent)