Summarising everything that the gospels say about Baptism in the space of a blog is going to be very hard but here goes:
The majority of times that the Gospels mention baptism it is usually in connection with John the Baptist (Mark 1:4-9, Matthew 3:1-16, Luke 3:1-22.)What was John’s baptism? It was a “baptism of repentance for the forgiveness of sins” (Mark 1:4) and also it was a baptism that, along with John’s preaching, was to prepare the way of the Lord (Matthew 3:1-3). If we take these passages together, John the Baptist’s ministry and preaching was one where repentance was crucial. He wanted people to repent and, for John, baptism was a sign that a person had done just this.
The other major passage that mentions the practice of Baptism is Matthew 28:19. Now if we look at the Greek of Matthew 28:19
πορευθέντες οὖν μαθητεύσατε πάντα τὰ ἔθνη, βαπτίζοντες
αὐτοὺς εἰς τὸ ὄνοματοῦ πατρὸς καὶ τοῦ υἱοῦ καὶ τοῦ ἁγίου πνεύματος,
We see in this clause the main verb is “make disciples “(μαθητεύσατε). It is imperatival in its force meaning that as Christians Jesus is commanding us to make disciples. The other verbs “go” (πορευθέντες) and “baptising” (βαπτίζοντες) are participles meaning they are subordinate to the main verb which is to make disciples. This means that baptising and the verb go is defined in some sense by the main verb “make disciples”. So Christians “go” to make disciples and they baptise those disciples. Therefore here, as in the preaching and baptising ministry of John, baptism is strongly linked with repentance and being a disciple of Jesus. To put it more strongly, Jesus is linking Baptism with repentance in a way which says to have a legitimate baptism the person must have become a disciple.
Now we do see Jesus interacting with Children (e.g. Matthew 19:13-14). But not once in the four gospels do we see Jesus (or anyone else for that matter) baptising a child. This surely makes us pause to at least reconsider whether infant baptism is legitimate.
In conclusion, the evidence from the gospels is that a person believes and repents and then is baptised. This makes repentance and belief precursors to baptism. Therefore the gospels are in favour of believers baptism and silent on infant baptism.