What is the general procedure for when someone is admitted to a hosptal under suicide watch?

It varies: The main goal, of course, is to ensure that the individual is safe. So, the staff will periodically evaluate the patient to determine what sort of intervention is required to ensure safety. In addition, treatments will be offered to reduce distress and promote hopefulness or a belief that the distressing issues can be resolved. A general intervention is to stay with the patient at all times.

Close observation: I agree with dr. Smith about the intent and process of suicide precautions. I'd add that some patients are both suicidal and medically ill, and need to be on medical units at first. In these cases, someone stays constantly with the patient on the medical unit while receiving iv's, etc -- until stable enough to be moved to inpatient psychiatry. Therapy thus begins even before they arrive..