The anointing of the sick is a practice that finds its authority in James 5:13-15. The issue is that there is a two-fold approach to illness that ought to exist when a believer in Christ Jesus becomes sick. First is the issue of sin. Although it MUST be understood that not all sickness is a form of judgment for personal sin, some is. Consequently, believers who are ill do not have to beat themselves up to try to figure out what sin is causing their illness - some illnesses are a result of natural process (which itself is a result of the impact of depravity on the entire world). However, if God's Spirit is bringing a sin to mind, then that sin ought to be confessed and dealt with appropriately. Hence, God instructs those so struggling to "call for the elders of the church and they are to pray over him, anointing him with oil in the name of the Lord." Verse 16 states: "confess your sins to one another, and pray for one another so that you may be healed."
The other element involved in this process is the actual anointing with oil. It is our belief that this practice carries a partial reference to medical assistance - that is, that anointing with oil was in part a primitive medical treatment in addition to being symbolic. Today, we believe that God has provided medical technology to be used to His glory.
In regard to the liturgy used, our ministry is not given to liturgical formulas. We pray extemporaneously. I trust this is of assistance to you.