The references explain that the anointing oil was smeared, rubbed or poured. The recipient is chosen as when "Jesus summoned His twelve disciples" (Mt 10:1) or "the Lord appointed seventy other" (Lk 10:1). Next "He gave them authority . . . to cast them out, and to heal every kind of disease and every kind of sickness" (Mt 10:1). He also instructed to "heal those in it who were sick and say to them, The kingdom of God has come near to you" (Lk 10:9). They then were to "'Go into all the world'" (Mk 16:15) and "'In My name they will cast out demons'" (:17) and "'will lay hands on the sick, and they will recover'" (:18). It is said that this was Jesus commissioning them, which meaningfully applies to all believers. Consequently "many wonders and signs were taking place through the apostles" (Ac 2:43) and they "were anointing with oil many sick people and healing them" (Mk 6:13). Jesus had prophesied "'The works that I do, he will do also'" (Jn 14:12). But he emphasized it would be done "'in My name'" (Mk 16:17). Peter's command accordingly was "'In the name of Jesus Christ'" (Ac 3:6) but he cooperated by "seizing him by the right hand [and] raised him up" (:7). Additionally "'greater works than these he will do; because I go to the Father'" (Jn 14:12).
References explain anointing as a ceremony. One explained that shepherds rubbed oil on a sheep's head to protect it from insects. In the Bible it was considered a symbol of protection. When someone was anointed he was empowered for a task and needed defenses to carry it out. It is a choosing. "God anointed Jesus of Nazareth with the Holy Spirit and with power" (Ac 10:38). "It is God who establishes us with you in Christ, and has anointed us, and who has also put His seal on us and given us His Spirit as a guarantee" (2Co 1:21-22). But why would Jesus require the anointing when he was already God? "The Spirit of the Lord is upon me, because He hath anointed me to preach . . . [and] to heal" (Lk 4:18). When you believe "'you will receive power when His Holy Spirit has come upon you'" (Ac 1:8). "You were sealed in Him with the Holy Spirit of promise" (Eph 1:13). Documents were made official when a wax seal by a stamp was applied to them. You do not undergo a chemical change in your body when you become a "new creature" (2Co 5:17). But you do receive the "Spirit in our hearts as a pledge" (1:21). In Jesus' situation "God was with Him" (Ac 10:38).