Romans 6:3-5
3 Know ye not, that so many of us as were baptized into Jesus Christ were baptized into his death?
4 Therefore we are buried with him by baptism into death: that like as Christ was raised up from the dead by the glory of the Father, even so we also should walk in newness of life.
5 For if we have been planted together in the likeness of his death, we shall be also in the likeness of his resurrection:
Galatians 3:27
27 For as many of you as have been baptized into Christ have put on Christ.
Colossians 2:12
12 Buried with him in baptism, wherein also ye are risen with him through the faith of the operation of God, who hath raised him from the dead.
The above passages, which speak of being "baptized into Christ", and being "buried with Christ in baptism", are used to teach Baptismal Regeneration - the doctrine that water baptism washes away one's sins, and gives them the new birth.
In what sense are we "baptized into Christ", and is this compatible with Salvation by faith?
Very simply, these verses' reference to being "baptized into Jesus Christ" refers to being baptized into Christ's body, which we learn from elsewhere in Scripture, is a spiritual baptism:
1 Corinthians 12:12-13
12 For as the body is one, and hath many members, and all the members of that one body, being many, are one body: so also is Christ.
13 For by one Spirit are we all baptized into one body, whether we be Jews or Gentiles, whether we be bond or free; and have been all made to drink into one Spirit.
Above, we see that "by one Spirit are we all baptized into one body", and that spiritual baptism happens at the moment of faith in Christ, whereupon the believer is sealed with the Spirit:
Ephesians 1:12-13
12 That we should be to the praise of his glory, who first trusted in Christ.
13 In whom ye also trusted, after that ye heard the word of truth, the gospel of your salvation: in whom also after that ye believed, ye were sealed with that holy Spirit of promise,
This sealing with the Spirit "baptizes" us into the Body of Christ, which is the Church (Ephesians 1:22-23, Colossians 1:18, 1:24).
We are given indication in the passage in Colossians, especially, that this is a spiritual baptism, because it's in the context of a spiritual circumcision "made without hands":
Colossians 2:11-13
11 In whom also ye are circumcised with the circumcision made without hands, in putting off the body of the sins of the flesh by the circumcision of Christ:
12 Buried with him in baptism, wherein also ye are risen with him through the faith of the operation of God, who hath raised him from the dead.
13 And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with him, having forgiven you all trespasses;
Of course, water baptism is not "made without hands", because it's a physical symbol.
Also, contrary to a common claim by Baptismal Regenerationalists, this baptism of the Spirit does not come at the point of water baptism, because not only are we given explicit examples of people who had the indwelling of the Holy Spirit before being water baptized (Acts 9:17-18, 10:47), but the Scripture states repeatedly that we receive the Holy Spirit after faith, without mention of water baptism:
John 7:39
39 (But this spake he of the Spirit, which they that believe on him should receive: for the Holy Ghost was not yet given; because that Jesus was not yet glorified.)
Galatians 3:2, 14
2 This only would I learn of you, Received ye the Spirit by the works of the law, or by the hearing of faith?
14 That the blessing of Abraham might come on the Gentiles through Jesus Christ; that we might receive the promise of the Spirit through faith.
Above, we see faith as the criteria for receiving the Spirit, just as we saw earlier in Ephesians 1:12-13. Interestingly, most Baptismal Regenerationalists also baptize infants, which cannot believe in Jesus, and pretending that they can opens up a true theological can of worms, as if they can, then they are culpable when they don't - and John 3:36 becomes just one of many verses that must be applied to innocent (Deuteronomy 1:39, Romans 7:9) children.
Continuing on, we can see that the immediate context of the passage in question from Galatians chapter 3 connects faith with the new birth, and the spiritual baptism being discussed:
Galatians 3:26-27
26 For ye are all the children of God by faith in Christ Jesus.
27 For as many of you as have been baptized into Christ have put on Christ.
Therefore, we "receive the Spirit" by faith, and that baptizes us into the Body of Christ. The water baptism that one does after faith is a mere symbol of that "one baptism" by the Spirit:
Ephesians 4:4-5
4 There is one body, and one Spirit, even as ye are called in one hope of your calling;
5 One Lord, one faith, one baptism,
The error that Baptismal Regenerationalists have in the passages in question, along with many of those used to explain them, is inserting "water" into all of these texts, when none of them mention "water".
Rather, they only mention a "baptism" - a word used in multiple senses, including as a euphemism for physical death (Matthew 20:22-23, Mark 10:38-39, Luke 12:50), and when used to refer to the "baptism of the Spirit", it is even contrasted with a water baptism (Matthew 3:11, Mark 1:8, Luke 3:16, Acts 1:5).
In summary, these verses speak to same clear testimony as the rest of Scripture - that we are given Eternal Life, the indwelling of the Holy Spirit, and are placed into the Body of Christ, when we put our faith in Jesus Christ.
The strange attribution of all the wonders of regeneration to the symbol meant to picture the actual operation, is as ridiculous as teaching that the bread and wine at the Lord's supper are actually Christ's body being offered, another false doctrine believed by most Baptismal Regenerationalists, discussed in this article.