The apostle Paul, in recounting his conversion experience to King Agrippa, speaks of the same things in Acts 26:19-20 (NKJV) (emphasis mine):
19 “Therefore, King Agrippa, I was not disobedient to the heavenly vision [I received on the road to Damascus], 20 but declared first to those in Damascus and in Jerusalem, and throughout all the region of Judea, and then to the Gentiles, that they should repent, turn to God, and do works befitting repentance.
Acts 26:19-20 (NIV 1984) (emphasis mine):
19 "So then, King Agrippa, I was not disobedient to the vision from heaven [I received on the road to Damascus].
20 First to those in Damascus, then to those in Jerusalem and in all Judea, and to the Gentiles also, I preached that they should repent and turn to God and prove their repentance by their deeds.
Basically anyone can say he has repented, but only his deeds will prove that true repentance has taken place. This is illustrated by Jesus' words in Matthew 7:24-26 (NKJV) (emphasis mine):
24 “Therefore whoever hears these sayings of Mine, and does them, I will liken him to a wise man who built his house on the rock: 25 and the rain descended, the floods came, and the winds blew and beat on that house; and it did not fall, for it was founded on the rock.
26 “But everyone who hears these sayings of Mine, and does not do them, will be like a foolish man who built his house on the sand: 27 and the rain descended, the floods came, and the winds blew and beat on that house; and it fell. And great was its fall.”
John the Baptist gave instruction to those who asked him what they should do in Luke 3:7-14 (NKJV) (emphasis mine):
7 Then he said to the multitudes that came out to be baptized by him, “Brood of vipers! Who warned you to flee from the wrath to come? 8 Therefore bear fruits worthy of repentance, and do not begin to say to yourselves, ‘We have Abraham as our father.’ For I say to you that God is able to raise up children to Abraham from these stones. 9 And even now the ax is laid to the root of the trees. Therefore every tree which does not bear good fruit is cut down and thrown into the fire.”
10 So the people asked him, saying, “What shall we do then?”
11 He answered and said to them, “He who has two tunics, let him give to him who has none; and he who has food, let him do likewise.”
12 Then tax collectors also came to be baptized, and said to him, “Teacher, what shall we do?”
13 And he said to them, “Collect no more than what is appointed for you.”
14 Likewise the soldiers asked him, saying, “And what shall we do?”
So he said to them, “Do not intimidate anyone or accuse falsely, and be content with your wages.”
Actually doing what God says is also mentioned in Ezekiel 33:30-32 (NKJV) (emphasis mine):
30 “As for you, son of man, the children of your people are talking about you beside the walls and in the doors of the houses; and they speak to one another, everyone saying to his brother, ‘Please come and hear what the word is that comes from the Lord.’ 31 So they come to you as people do, they sit before you as My people, and they hear your words, but they do not do them; for with their mouth they show much love, but their hearts pursue their own gain. 32 Indeed you are to them as a very lovely song of one who has a pleasant voice and can play well on an instrument; for they hear your words, but they do not do them."
The people loved to hear Ezekiel speak, as if he was a great musician or singer, but they would not actually do what he said. Read Ezekiel 18 to find more concrete examples of what to do and not to do, such as:
- don't defile your neighbor's wife (v6)
- don't rob anyone (v7)
- give bread to the hungry (v7)
- do not exact usury (v8)
Jeremiah has similar words in Jeremiah 7:1-11, such as:
- thoroughly execute judgement between a man and his neighbor (v5)
- do not oppress the stranger, fatherless, or widow (v6)
- do not shed innocent blood (v6)
- do not steal, murder, commit adultery, or swear falsely (v9)
The above examples are not a complete list, and I encourage you to read the full passages. I also encourage you to read other passages such as the Ten Commandments in Exodus 20, Leviticus 18-19, Matthew 5-7, and 1 Corinthians 6:9-11 to get more of the concrete examples you seek. And if you have more questions about these passages or others you may run across, don't hesitate to come back and ask them! :)
To answer your second question (using your own words), these actions are in part required for salvation in the sense of simply being evidence of living a Christian life. If certain actions were required for salvation, then it would be possible to "earn" your way to heaven and belief (or faith) in Jesus would not be required. True Christians are those who want to keep God's commandments out of love for Him, not wanting to do anything that He doesn't like.
After all, Jesus himself said, "If you love Me, keep My commandments" (John 14:15 NKJV). This is reiterated in 1 John 2:3-4 (NKJV): "3 Now by this we know that we know Him, if we keep His commandments. 4 He who says, 'I know Him,' and does not keep His commandments, is a liar, and the truth is not in him."
Finally, you asked for commentary references, so here are a few.
Snippet from John Gill on verse 14:
it is clear that the apostle is not speaking of true faith, [...] but of a profession of faith, [...] by which a man...only says he has faith, but has it not....
Snippet from Adam Clarke on verse 14:
As the Jews in general were very strenuous in maintaining the necessity of good works or righteousness in order to justification, wholly neglecting the doctrine of faith, it is not to be wondered at that those who were converted, and saw the absolute necessity of faith in order to their justification, should have gone into the contrary extreme.
Snippet from Albert Barnes on verse 14:
[The apostle] doubtless had in his eye those who abused the doctrine of justification by faith, by holding that good works are unnecessary to salvation, provided they maintain an orthodox belief.
A large collection of other commentaries can be found at StudyLight