Admission comes with the Duomo ticket and it's located in the Palazzo Reale complex directly to the…read moresouth of the Duomo (to the right, if you're in front of, and facing the Duomo) as many have mentioned.
When you're facing the front of the Palazzo Reale, there is a main archway in the center, and the duomo museum entrance is within that archway, on the left side. (One of the entrances to the Palazzo Reale exhibitions is on the right side). There is also a cafe directly to the right of the duomo museum entrance.
You can purchase a separate ticket here if you didn't purchase a duomo ticket too, though I agree with some other reviews in that it might not be worth your 45min-1hr if you have only limited time in Milan. There are a lot of relicts on display from mosaics and church objects to tapestries, antique books, carvings and sculptures. Many of these have detailed explanations for individual objects in Italian, with a fair amount in English too, though some might feel a need more background. It's possible to get a multimedia guide via their app (€3.49 downloadable on google play or App Store) that takes you thru the museum.
The walking trajectory within the museum is rather winding, they loop you around using lots of arrows and "exhibit continues this way" signs, I guess they make the most of the space. I appreciated the miniature wooden models of the Duomo were impressive in the level of detail. Also insightful to see some of the stone sculptures that were part of the outer facade--each work can be considered a masterpiece in itself.
On a Sunday afternoon in April it wasn't too crowded, though certain rooms more than others especially with tour groups, and barely a line to enter. (Contrasted with a 1 hour wait at the Impressionist exhibit at the Palazzo Reale). There were bathrooms inside but small so there was a line for those.