When you realize that the Bible speaks of every individual Christian as part of "the Church" and that every individual Christian is indwelt with the Holy Spirit, then you will begin to understand.
The first account of how the Holy Spirit dealt with the new Christians gathered together for prayer and worship in Jerusalem (50 days after the Sabbath of Passover week) is in Acts chapter 2. Read all of it and see how the outpouring of the Holy Spirit happened, as Jesus promised it would after He'd returned to Heaven. That spectacular anointing enabled some 3,000 converts to be joined to the Church after Peter's inspired preaching about the death and resurrection of Christ. From then on, every convert to Christ received the indwelling Holy Spirit as confirmation that they now belonged to Christ by faith, and that they would join Him for eternity. See Romans chapter 8, first half for that, and this scripture:
"And you also were included in Christ when you heard the word of truth, the gospel of your salvation. Having believed, you were marked in him with a seal, the promised Holy Spirit, who is a deposit guaranteeing our inheritance until the redemption of the purchased possession - to the praise of his glory." Ephesians 1:13
That is what it means to have the Holy Spirit in the Church - each Christian who belongs to Christ belongs to the one Church He builds, which the gates of Hades will not overcome (Matthew 16:18). This has nothing to do with denominations. The gathered Church is on Earth, made up of all believers at all times in all nations, and that Church continues in the presence of the risen Christ. One day it will all be gathered and beautified as a bride, and the Holy Spirit is involved in that process of sanctification of all the members of that spiritual 'body'. 2 Corinthians 4:13-15.