The Anointing of the Sick is one of the sacraments of healing in the Catholic Church (the other being Reconciliation). It may be administered to any Catholic who comes into danger because of sickness or old age. Anointing is not the “Last Rites,” although that is the popular opinion of this Sacrament. While it may be received prior to death, often in conjunction with Reconciliation and the giving of Holy Communion, it can be received multiple times during a person’s life. While you should be gravely ill to ask for the sacrament, or about to have an operation (always a grave medical issue from a religious viewpoint), you do not have to be in danger of death.
To request Anointing of the Sick, speak with a priest after Mass or call the Church office at 405-722-2110. If this is an emergency in Oklahoma City call 405-722-2110 and press 4.
Each hospital also has a Catholic priest assigned to it who can be contacted by hospital staff in an emergency. It is generally best, however, to not wait until the last minute.