Matthew 28:19
19 Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
Baptism is to be performed in the name of all three Persons of the Trinity - Father, Son, and Holy Spirit. Additionally, the "name" is singular, yet three are mentioned, because there is one Essence, yet there are three Persons.
"In the name of" is an idiom which means "by the authority of", or "on behalf of", or "in accordance with the will of" (Deuteronomy 18:5-7, 18:20-22: 1 Samuel 17:45, 25:9: 2 Samuel 6:18: 1 Kings 22:16: 2 Kings 2:24, Psalm 118:10-12, 129:8, Micah 4:5, Matthew 10:41-42, 21:9, 23:39, Acts 2:38, 3:6, 9:27: 1 Corinthians 1:13, etc.). Additionally, the fact that "name" is singular does not mean that one thing is being referred to, as "name" is used as a plural referring term throughout Scripture (Genesis 48:16, Exodus 23:13, Deuteronomy 18:20, Joshua 23:7, Ruth 1:2: 2 Samuel 7:9: 1 Chronicles 17:8, Proverbs 10:7, Luke 6:22). Therefore, an assertion that the word "name" being singular is indicative of Jesus and God being one subject misunderstands the meaning of this idiom.
How do Unitarians understand three things being mentioned here - the Father, Son, and Holy Spirit? If the Spirit is the power of the Father, as many Unitarians believe, there would only be two subjects - God and His Messiah. So, why mention the Holy Spirit, if God is already mentioned?
The answer would be that God's Spirit is often spoken of distinctly in the New Testament, and is emphasized as how God is acting in the world, after the ascension of His Messiah. Jesus promised the Spirit to His Apostles (Luke 24:49, John 14:26), believers are said to be sealed with the Spirit (Ephesians 1:12-14), and indwelt by the Spirit (1 Corinthians 6:19), and the Apostle Paul writes, that "by one Spirit are we all baptized into one body" (1 Corinthians 12:13). So, in the passage in question from Matthew chapter 28, Jesus would be reiterating to believers that they are to be baptized as followers of His, under the authority of God, and endeavoring to walk in His power. Other Unitarians may express their understanding of this passage slightly differently, but in general would largely be in agreement with this.
Some Unitarians, especially historically, have believed that the Holy Spirit is a lesser divine Being, created by God the Father, in addition to Jesus Christ. This view would maintain that the Father, Son, and Spirit are mentioned in this passage because they are three distinct entities. However, this would be a minority view amongst most Unitarians today.
In summary, believers are baptized as followers of Jesus Christ, who are sealed with the Spirit of God, and who intend to walk in the power of God. This "one baptism" (Ephesians 4:5) was an important source of unity within the early Church (1 Corinthians 1:11-15), and Jesus instructed His followers to maintain this practice, which is why it is seen in the book of Acts, and in the Epistles.