The church was started when Jesus came down to die for our sin. He helped pave the way for this new church. He incharged his apostle and followers to help spread the good news. The quote above shows Jesus naming Peter as the first Pope, the first leader of the church. God sent the Holy Spirit during Pentecost to ignite Peter, Paul and all the other disciples, this helped them spread Jesus' message and help bring people to the faith. Paul and John both had a big part in spreading the gospel and with their help Christianity spread.
Jesus told his followers what to do and this is known as The Great Commission. To spread all these ideas the Apostles went on missionaries. The word mission comes from the word missionem meaning "act of sending" in Latin. This name is appropriate because missionaries are groups of people that are sent to a specific area to preform religious services. And from the religious services that Jesus taught them they were able to build the church and enforce the sacraments.
"I KNOW YOUR DEEDS, THAT YOU ARE NEITHER COLD NOT HOT. I WISH YOU WERE EITHER ONE OF THE OTHER! SO, BECAUSE YOU ARE LUKEWARM - NEITHER HOT NOR COLD - I AM ABOUT TO SPIT YOU OUT OF MY MOUTH". REVELATION 3:15-16.