What are the rules for using apostrophes?

Hello! Thank you for the question and for providing the worksheet that you are working with.
As the worksheet says, an apostrophe can be used to indicate that an item or items belong to someone, a group of people, something or a few things. I'd like to highlight three examples in the worksheet that you attached:
1. "Sarah's textbook was in her backpack" - the textbook belongs to Sarah and so we will add 's to owner Sarah - in this example, both Sarah and the textbook are in the singular. 
2. "The team's jerseys were brand new" - the jerseys (plural) belong to the team (singular), and so 's is added to the owner, the team. If there was more than one team, in other words, if there were teams (plural) then you would just add an apostrophe, and it would look as follows: "The teams' jerseys were brand new". This difference is highlighted in the third example.
3. "The students' desks were very clean" - The desks (plural) belong to the students (plural) and so you will add an apostrophe to the owners, the students. 

In conclusion, the apostrophe is used to show ownership. All of the sentences in the worksheet are speaking about ownership. Therefore the options with the apostrophe will be the correct answers. 

I hope that this helps you!