There are different ways to visit the Vatican museums which include the Sistine Chapel.
1. You can book a online ticket directly from The Vatican Ticket office
At the time of this writing, the cost is as follows adults 17€, children (6 - 17 with valid ID) and students (under 25 with valid ID) 8€. Plus 4€ per person booking fee.
This gives you a fast track time stamped entrance to the Museums. You can explore the museums at your own pace and you will be able to visit the Sistine Chapel.
This ticket does not give you access to St. Peter's Basilica. If you would also want to visit St. Peter's Basilica once you finish your visit you will have to line up in St. Peter's square to pass security. Entrance is free. The security line is typically 1 hour to 2 hours long depending on the time of day and season.
Vatican Ticket office link here.
2. You can wait in line at the museums
The line is typically 2 hours to 3 hours long depending on the time of day and season. At the time of this writing, the cost is as follows adults 17€, children (6 - 17 with valid ID) and students (under 25 with valid ID) 8€.
3. If the Vatican ticket office is sold out you can purchase tickets through tour operators
You will pay for the entrance tickets plus a premium.
This gives you a fast track time stamped entrance to the Museums. You can explore the museums at your own pace and you will be able to visit the Sistine Chapel.
This ticket does not give you access to St. Peter's Basilica. If you would also want to visit St. Peter's Basilica once you finish your visit you will have to line up in St. Peter's square to pass security. Entrance is free. The security line is typically 1 hour to 2 hours long depending on the time of day and season.
4. Or you can go the tour route
A Vatican Tour is a 2 - 3 hrs guided tour that includes the highlights of the museums, Sistine Chapel and your tour guide escorts directly to St. Peter's Basilica via a tunnel reserved for tour guides. With this tour you will SKIP ALL THE LINES AT THE VATICAN.