In John 13 Jesus gives an example of serving by modeling it. He modeled it by washing the dirty feet of his disciples. Here are some observations about the passage.
V1 Jesus knew his hour was come. It's interesting that this passage about being a servant comes not long before his hour. "His hour" refers to the cross and drinking the cup of wrath.
V2 Jesus embarked on serving knowing his traitor was in the room and would soon betray him. How apt are we to serve someone we know is betraying us?
V3 Jesus was able to serve because he knew the Father gave him the disciples, that he was sent from the Father and going back to the Father. When we're in fellowship with God and secure in our being sent by God we're able to serve. Sometimes we have a hard time serving because we're comparing ourselves to others or looking at others.
V4-11 Jesus modeled serving by taking on the role of a servant. In reality the roles should have been reversed. The disciples should have been lined up to wash Jesus' feet. But, Jesus wanted to give a practical object lesson.
V12-16 Jesus asks the disciples if they understand what he's just done. If Jesus as their Lord and Master has washed their feet and they are co-servants of Christ then they too should be able to humble themselves to wash each others' feet. This is important because Jesus is leaving soon and they will only have each other and they need to be able to serve each other.
V17 The clincher and practical application is this...if you know these things and DO them you will be happy. There is blessing and fulfillment attached to being a servant.