If you don't have a Bible handy, you can read Acts 1 online here:
Acts Chapter One (NIV)
Acts Chapter One (NASB)
Verses 1-11: Luke reviews Jesus' post-resurrection teaching and ascension. Jesus promises that the disciples would receive power when the Holy Spirit comes.
Verses 12-26: The disciples prepare for their work. They devote themselves to prayer and select candidates to replace Judas as a witness to Christ's resurrection.
II. KEY PASSAGES
(A) Acts 1:1--Luke says that his Gospel covered what Jesus "began to do and teach." The word "began" indicates that Jesus' teaching and works in the Gospel of Luke were just the beginning. The risen Lord would continue to teach and work through His body, the church. In the Gospel of John, Jesus told the disciples that they should rejoice, because He was returning to the Father (14:28), where He would prepare a place for them (14:2), answer their prayers (14:13), and live within His followers (17:26).
(B) Acts 1:3--Jesus presented Himself alive to His disciples "by many convincing proofs." This would be strange if faith were contrary to evidence (as some claim today). Acts 1:3 and many other passages show that Biblical faith is rooted in evidence.
(C) Acts 1:7-8, 11--Jesus says that the disciples weren't given specifics as to God's future acts, but that they would receive power to do the work they had been given. Similarly, the angel asks why the Apostles were staring into the sky, when they clearly had work to do. The Bible gives us some clues about the end times; however, the opening chapter of Acts teaches us that we shouldn't have an unhealthy interest in figuring everything out. Instead, we should focus on the work that God has given us.
(D) Acts 1:24-26--The disciples pray to Jesus to choose a disciple to replace Judas. Since Jesus had chosen all of the disciples, it was important that He choose Judas' replacement as well. This passage (and several others in Acts) is confirmation of Jesus' claim in John 14:13 that He would be able to answer their prayers after returning to the Father. (Note to Muslims: What mere prophet can answer prayers?)