“The Lord said to my Lord.” The quotation is from Psalm 110:1, and it is quoted by Jesus in Matthew 22:44; Mark 12:36, and Luke 20:42-43. Psalm 110:1 is a very important verse theologically. For one thing, it shows that Jesus is not equal to God (see commentary on Psalm 110:1).
[For more information on Jesus not being God, see Appendix 10, “Jesus is the Son of God, Not God the Son,” and Appendix 11, “What is the Holy Spirit?”]
“by the holy spirit.” David spoke as God directed him to via the gift of holy spirit that was upon David (see commentary on Matt. 22:43). Even though the Greek has both articles with holy spirit, tō pneuma tō hagion (τῷ πνεύματι τῷ ἁγίω), it seems to be more of a reference to the gift of holy spirit than it is to the Giver, God. There are many other times the gift of holy spirit has both articles (cp. Luke 3:22; John 14:26; Acts 2:33; 5:32; 10:44, 47; 11:15; 15:8; 19:6; Eph. 1:13; 1 Thess. 4:8).
[For more information on the uses of “Holy Spirit”, see Appendix 6: “Usages of ‘Spirit.’” For more information on the Holy Spirit, see Appendix 11: “What is the Holy Spirit?”]