For what length of time would my friend stay in the psychiatric ward?

It depends: This depends on the illness your friend has, what treatments are needed, and how well s/he responds. Other considerations outside of actual medical need, unfortunately, may include what his/her insurance company will agree to "authorize.".

Depends: Can range from a few days to months, depending on the illness. Usually patients can be discharged when they are no longer a risk to their own safety or that of others, and can adequately care for themselves in the environment to which they are being discharged.