David was anointed 3 times to be king

[tonychanyt]

1. Samuel anointed the young (probably teenage) David in 1 Samuel 16:

12b the LORD said, “Arise, anoint him, for this is he.” 13a Then Samuel took the horn of oil and anointed him in the midst of his brothers. And the Spirit of the LORD rushed upon David from that day forward.

2. Some 12 years later, the Philistines killed Saul. The men of Judah anointed David in 2 Samuel 2:

3 David brought up his men who were with him, everyone with his household, and they lived in the towns of Hebron. 4 The men of Judah came, and there they anointed David king over the house of Judah.

Who specifically actually did the anointing?

It was probably a local leader of Judah at Hebron. Similarly, some centuries later, the people of Judah anointed Jehoahaz (2K 23:30).

3. Two years later, the other tribes anointed David in 2 Samuel 5:

3 So all the elders of Israel came to the king at Hebron, and King David made a covenant with them at Hebron before the LORD, and they anointed David king over Israel.