When South Africa’s apartheid government ended, the country was in possession of at least six nuclear weapons. Where were they stored and how were they assembled?

They were stored in storage vaults at the Kentron Circle facility, which was about 15 km from the main South African nuclear center at Pelindaba. You can see photos of the facility and the vaults here.

They were gun-type HEU weapons, with the fissile material stored in two pieces. The bombs themselves had a "front end" and a "back end" that contained the fissile material and other components. The front and back ends were kept in different vaults, not assembled into a weapon, for control, security, and safety reasons.

To assemble a weapon, you'd need to install the front and back ends into the overall weapon assembly, and presumably check all of the wiring and so on. The weapons did not use initiators so there aren't any limited-use components. So presumably the assembly could happen relatively quickly.

You can get a lot more details in David Albright's Revisiting South Africa's Nuclear Weapons Program: Its History, Dismantlement, and Lessons for Today (2016).