"The eunuch was reading this passage of Scripture: 'He was led like a sheep to the slaughter, and as a lamb before the shearer is silent, so he did not open his mouth. In his humiliation he was deprived of justice. Who can speak of his descendants? For his life was taken from the earth.' The eunuch asked Philip, 'Tell me, please, who is the prophet talking about, himself or someone else?' Then Philip began with that very passage of Scripture and told him the good news about Jesus." NIV translation
What an example we have here of how we are to share the gospel. The Ethiopian was reading from the scroll of Isaiah the prophet. You have to understand that, at this time, there was no "Bible" like we have today. Even having a piece of the Old Testament such as this would have been a big deal. The eunuch had the scripture and could read it but did not know that it was referring to Jesus.
Philip started with what the Ethiopian had and told him about Jesus. That is the same thing that we, as Christians, are called to do.
The passage that the Ethiopian was reading is so powerful and describes Jesus' actions so well yet was written a long time before Jesus came to the earth. That, my friends, is what God can do!
"As they traveled along the road, they came to some water and the eunuch said, 'Look, here is water. Why shouldn't I be baptized?' And he gave orders to stop the chariot. Then both Philip and the eunuch went down into the water and Philip baptized him." NIV translation
In this passage, we see faith put into action. When the Ethiopian heard the gospel of Jesus Christ, his heart was changed. Then, he immediately followed with obedience by being baptized. Notice that, in the passage, Philip did not have to tell him to be baptized. It was the eunuch that said "Why shouldn't I be baptized?" It is a good example for us in that, when we come to Christ, we should learn that is followed by obedience.
"When they came up out of the water, the Spirit of the Lord suddenly took Philip away, and the eunuch did not see him again, but went on his way rejoicing. Philip, however, appeared at Azotus and traveled about, preaching the gospel in all the towns until he reached Caesarea." NIV translation
In this passage we see that, after Philip had done what God wanted him to do in the situation, God took him to the next place where he needed to be. In this case, the Spirit took him immediately. Then, Philip went about his next task in his next area.
That is much the same way that we should be. We serve where God has us until He tells us to move on. Then, we simply do what He asks us to in the next place or situation. In order to do that, we must first pray and listen to what God tells us to do.