Book a timed entry on the official site, go to the Museums entrance on Viale Vaticano at that time, and follow the route; the chapel comes after the galleries and the Raphael Rooms, which is why the Museums say to allow time and why final entry is 6:00 p.m. even though the galleries stay open to 8:00 p.m. Monday to Saturday. On the free last Sunday of the month (9:00 a.m. to 2:00 p.m., final entry 12:30 p.m.) the chapel is included but the crowds are heaviest.
The Museums also sell early-entry and guided options that reach the chapel before general opening; those are the only official way to see it with fewer people. The chapel is closed when the Museums are closed, on ordinary Sundays and on the Vatican holidays listed on the hours page, and it is closed to the public during a conclave or a papal ceremony held there.
Tickets are not refundable, so match the date to your Rome schedule before paying. The existing page is-the-sistine-chapel-inside-st-peters-basilica explains why you cannot reach the chapel from the basilica, and can-i-take-photographs-in-the-sistine-chapel covers the no-photo rule.