Standing when he processes into the church. Standing when he goes up into the sanctuary and to the tabernacle. Kneeling when he opens the tabernacle and removes the luna. Remain kneeling as he places the luna in the monstrance. Hopefully he then incenses the monstrance, kneeling himself. Our priests and deacons do this from a kneeler placed at the foot of the altar.
It's the reverse on a benediction and reposing of the host. The people are kneeling the entire time, and stand when the priest or deacon close the tabernacle door after placing the luna inside.