When you say you already have tickets, I'm going to assume you mean the tickets for the ferry. Are you leaving from the NY dock or the NJ dock?
Are you taking the subway to catch the ferry or driving?
Assuming you are leaving from NY, you need to arrive about 30 minutes or so before sailing time. There is a line for a security check (similar to airport security, but no naked body scanners or restrictions on taking water
)
For people who haven't bought advanced tickets there will be another long line to get into the courtyard of Castle Clinton to buy tickets. However, there are exhibits and a gift shop inside the fort that you can visit as well.
The area around where you catch the ferry is a park called Bowling Green and it will be filled with street performers, people selling knock off handbags and watches, and there are lots of green space to eat a picnic lunch. You could also take your lunch and eat on Liberty Island, but there is little shade and limited tables for the snack counter in the gift shop on the island.
Once you catch the ferry your first stop (if you leave from NY) is Liberty Island. There is a small Visitors Center, gift shop and snack bar. You can walk all the way around the statue for photos and different views. If you have already pre arranged for a special ticket you can get into the base or even go up to the crown, if not you are not allowed up.
The ferries run about every 20 minutes and you will leave Liberty Island and next stop at Ellis Island. The self guided tour of Ellis Island can easily stretch for 2-4 hours. You can walk in the foot steps of an immigrant though the great hall, medical checks, etc. See exhibits on what people carried with them to start their new life in America and even research your family to see if any of your ancestors passed though Ellis Island.
All in all plan on spending 2-6 hours.
If you arrive early or find you have extra time, a short walk from where you catch the ferry to Liberty Island is the building where you can catch the ferry to Governor's Island. This ferry is free and run by the National Park Service and Governor's Island is a neat and less crowded place to visit. You can also ride the Staten Island Ferry for free and get a nice view of the Statue of Liberty as you pass it.
A short walk or subway ride away and you can see Wall St (the Bull statue) and Ground Zero.