Cessationist teachings are that the free gift of the Holy Spirit that God gave at Pentecost, as prophesied by the Prophet Joel somehow... ceased.
Sometime in the first century.
Or something.
No, that isn't what cessationism teaches. It is that certain GIFTS of the Holy Spirit - especially the "sign" gifts - ceased sometime after the Apostolic era. The indwelling of the Holy Spirit happens when one believes on the Lord Jesus Christ and are born again into God's family. In fact, we are sealed with Holy Spirit until the day of redemption (see Ephesians 4:30). The gift of God is eternal life through Jesus Christ our Lord. Each believer is then given gifts by which the body of Christ is edified and Jesus is glorified. We have different gifts according to the grace given us (Romans 12:6). All these are the work of one and the same Spirit, who apportions them to each one as He determines. (I Cor. 12:11).