"Again, the next day, John stood with two of his disciples. And looking at Jesus as He walked, he said, 'Behold the Lamb of God!' The two disciples heard him speak, and they followed Jesus. Then Jesus turned, and seeing them following, said to them, 'What do you seek?' They said to Him, 'Rabbi' (which is to say, when translated, Teacher), 'where are You staying?' He said to them, 'Come and see.' They came and saw where He was staying, and remained with Him that day (now it was about the tenth hour). One of the two who heard John speak, and followed Him, was Andrew, Simon Peter's brother. He first found his own brother Simon, and said to him, 'We have found the Messiah' (which is translated, the Christ). And he brought him to Jesus. Now when Jesus looked at him, He said, 'You are Simon the son of Jonah. You shall be called Cephas' (which is translated, A Stone)" (John 1:35-42).
John the baptizer looked at Jesus again and proclaimed Him to be the Lamb of God. John was properly focused on Jesus, not himself. If one does not first focus on Christ, such a one will never be able to faithfully proclaim Him.
Who were the two disciples who were with John the baptizer? One is specifically identified as Andrew and the second, since he is not named, is most likely John (the son of Zebedee). As far as is recorded, this is the last time John the baptizer would see Jesus. When they heard John's words, these two disciples followed Jesus. The goal of all preachers should be to proclaim Christ, and the response of all listeners should be to follow Christ rather than a fallible preacher (cf. John 1:37; 3:26ff).
Jesus noted that they were literally following Him around. Undoubtedly, they felt such awe and reverence for Jesus that it caused them to be hesitant to address Him. Thus, Jesus Himself breaks the ice (so to speak) by asking in return - "What do you seek?" The disciples probably didn't know, so they ask Him a question - "Where are you staying?" Jesus invites them to "Come and see" where He was staying. John wrote in Roman time, and therefore "the tenth hour" likely means 10 A.M. In other words, Andrew and John spent most of the day with Jesus. As a side note, there are several translation explanations found in this context, indicating the book was not primarily intended for a Jewish audience.
So what did these three men do and talk about all day? Few details are given, although we do know that it wasn't a group of three for very long. Before he did anything else, Andrew "first" went and found his brother, Simon Peter, and told him about Jesus. This shows how important this was to Andrew (and sets a marvelous example for all today regarding bringing our loved ones to Christ). Andrew is witness #2 - "We have found the Messiah", he said. Messiah is a Hebrew term which is equivalent to "Christ" in Greek and it means "the anointed one" in English.
Andrew brought Peter to the Lord. It takes love, dedication, and courage to bring someone to Christ, but Andrew did it, and the Lord expects His disciples today to do it as well (cf. Matt. 28:19,20).