You drop off the box and they wire it up and give you remote console access. You can even schedule an on-site meeting with your equip as needed. Some colo partners will also keep replacement parts for you like if a disk or power supply goes bad.

As others have mentioned, there's usually a remote hands feature that you can contract out. If you wanted to, many colos will rack and wire up all your equipment for you, for a cost. It really depends on how much you're wanting to offload on to the provider. They might do it all for you, they might just give you a cabinet or cage with power and a network drops.

You can usually pay the data center staff for their time to push a button or connect a few wires. Seems expensive at first when they quote you 50€/15 minutes but often way cheaper than somebody driving there and going through security to do the same.

Unless you don't want strangers touching your assigned rack, then you need to bring the key.

In addition to the other comments, after it's up & running some colos will also offer "remote hands" assistance, like replacing a failed drive. In that case ideally the enclosure will or can be made to make that slot's LED red or something so they know exactly which drive to pull.