It is there by example.
On hearing this, they were baptized in the name of the
Lord Jesus. When Paul placed his hands on them, the Holy Spirit came
on them, and they spoke in tongues and prophesied.
The new disciples operated initially in the gift through the laying on of the apostle's hands. Likewise, this is corroborated by Acts 8.
Acts 8:18-19 (emphasis mine)
When Simon saw that the Spirit was given at the laying on
of the apostles’ hands, he offered them money and said, “Give me
also this ability so that everyone on whom I lay my hands may receive
the Holy Spirit.”
While it does not list tongues here, it is similar enough to the previous that many infer it. Simon's response was wrong, but his observation was right (bold).
While there are two examples of God doing this without human intervention, such as in Acts 2 at Pentecost and Acts 10, this is the exception, not the rule.
While Peter was still speaking these words, the Holy Spirit came on
all who heard the message. The circumcised believers who had come
with Peter were astonished that the gift of the Holy Spirit had been
poured out even on Gentiles. For they heard them speaking in
tongues and praising God.
The sign to the Jews that the Gentile believers had received as well was them speaking in tongues.
While this and Acts 2 were sovereignly initiated by God Himself, Hebrews 6:1-2 lists the "laying on of hands" as a foundational doctrine of the church, without with one cannot go on to maturity.
The proper example, then, to how to receive the gift, according to the first century church, is through the laying on of hands of those who have been equipped to do so.
This is corroborated by 2 Timothy 1:6, where Timothy possessed a gift through the laying on of hands, and likewise 1 Timothy 4:14, where a gift had been given through the laying on of hands by the elders.
This also demonstrates that it need not be one of the apostles, but, by extension, leaders in the church.