The museum entrance is west of the Arch, facing the Old Courthouse. Look for the low arc of glass and stainless steel set into the ground, rather than trying to enter through an Arch leg. The legs serve as exits. This small piece of orientation saves an unnecessary walk, especially when you have a timed tram reservation.
The entrance also explains the architecture of the renewed museum. Cooper Robertson and James Carpenter Design Associates, working with Trivers, expanded the underground building toward the city. Their low, curved frontage echoes the Arch's material and geometry without trying to compete with its height. From outside, the land still reads as a park; inside, daylight and views back toward downtown make the arrival feel connected to the surface.
Entry to the museum is free and does not require a ticket, although visitors still go through security screening. Buying a tram ride, film or other paid activity is a separate decision. If tickets to the top have sold out, or a member of your group cannot use the tram, the principal historical exhibition is still available. That distinction is easy to miss on a website arranged around ticket packages.