How is a open heart transplant performed?

Carefully! Seriously though, the patient is placed on cardiopulmonary bypass, the donor heart is readied, the recipient heart is arrested and removed - usually the back walls of the atria are left behind, that is where the new heart is grafted. Immunosuppressant may be given and the patient is weaned off bypass and the donor heart takes over.
You mean heart trans. You mean heart transplant. The old heart is removed and the new one is placed in.