Acts is addressed to Theophilus, and it picks up where "the first book" ended, with the risen Jesus teaching his apostles for forty days about the Kingdom of God. He commanded them to stay in Jerusalem and wait for the promise of the Father, for they would be baptized in the Holy Spirit not many days from then (Acts 1:5).
The apostles still asked about a restored kingdom for Israel. Jesus redirected them: the times and seasons are set by the Father's own authority, but they would receive power when the Holy Spirit came upon them. Acts 1:8 then works like a map for the whole book: witness in Jerusalem, in all Judea and Samaria, and to the uttermost parts of the earth.
As they watched, Jesus was taken up and a cloud received him out of their sight. Two men in white clothing asked why they stood looking into the sky, and said that this Jesus would come back in the same way they saw him go.
The waiting was not idle. The group of about one hundred twenty continued with one accord in prayer. Peter said Scripture had to be fulfilled about Judas. A man who had been with them from John's baptism until Jesus was taken up must become a witness of the resurrection. They put forward Joseph called Barsabbas and Matthias, prayed to the Lord who knows the hearts of all men, and drew lots; the lot fell on Matthias, who was counted with the eleven apostles.