Who exercises the oversight
You assign human oversight to natural persons who have the necessary competence, training and authority, and who get the necessary support [1]. Authority means that the person may actually deviate from the outcome.
What that person must be able to do
The system must be supplied so that the person overseeing it understands its capacities and limitations and can monitor its operation, remains aware of the tendency to rely too much on the output, can interpret the output correctly and can, in any situation, decide to disregard or reverse the output [2].
Who arranges what
The provider designs the system so that effective oversight is possible [3] and determines which measures you carry out as a deployer [4]. You follow those measures and the instructions for use. These duties start on 2 December 2027 [5].
In practice
Appoint an owner per process, give them time and instruction to investigate deviating outcomes, and record how often the human decision deviates from the system. That shows that the oversight is real.