This sentence requires no punctuation.
Explanation: 
You could place a comma after "Tuesday," but omitting it is better because the introductory phrase is short and only slightly parenthetical.

"I really enjoyed `Lost Ground,' the new short story by William Trevor," said Samuel.
Explanation: 
If you are following North American usage, you need double quotation marks around the words spoken by Samuel and single quotation marks around the title of the short story, because it is a minor title and is already inside double quotation marks (in British usage you write the single quotation marks by default). The comma after "Ground" is necessary because the phrase that follows is non-restrictive, and the comma must fall inside the single quotation mark. The comma after "Trevor" is required to introduce "said Samuel" (this is a convention of dialogue), and the comma must fall inside the double quotation marks.

His form was excellent; his dive was superior to his other competitors' attempts.
Explanation: 
You need a semicolon to link the two independent clauses. Place the apostrophe after the "s" to show the possessive of the plural noun "competitors."

His form was excellent; his dive was superior to his other competitors' attempts.
Explanation: 
You need a semicolon to link the two independent clauses. Place the apostrophe after the "s" to show the possessive of the plural noun "competitors."

My sister's favourite foods are as follows: pepperoni pizza, applesauce, and strawberries.
Explanation: 
You need the apostrophe in "sister's" to show that the noun is possessive, the colon after "follows" because the clause preceding the colon is independent and introduces a list, and the comma after "pizza" because it is an element in the list. The comma after "applesauce" is optional.