Let us first clarify that the Holy Ghost and the Spirit of God are one and the same Spirit. A person who has God's Spirit has the Holy Ghost.
In Acts 19:2, Paul asked twelve men in Ephesus, 'Did you receive the Holy Spirit when you believed?' We must conclude from this question that it is possble for a person to believe but not yet be filled with the Spirit. We see this happening in Samaria where the Bible says in Acts 8:12, 'But when they believed Philip as he preached the things concerning the kingdom of God and the name of Jesus Christ, both men and women were baptized.' Notice that the way they believed was by being baptized. Acts 8:14-17 then says, 'Now when the apostles who were at Jerusalem heard that Samaria had received the word of God, they sent Peter and John to them, who, when they had come down, prayed for them that they might receive the Holy Spirit. For as yet He had fallen upon none of them. They had only been baptized in the name of the Lord Jesus.'
This passage shows that even though some believers have not yet received the Spirit, they need to. When Jesus spoke of 'living water,' John explained, 'This He spoke concerning the Spirit, whom those believing in Him would receive' (John 7:39). It is God's intention and promise that everyone who believes also receive the Spirit. This is what it means to be 'born of the Spirit.'
When Peter and John arrived in Samaria, the Bible says, 'Then they laid hands on them, and they received the Holy Spirit' (Acts 8:17). When Paul laid hands on the twelve men in Ephesus, the Bible says, 'The Holy Spirit came upon them, and they spoke with tongues and prophesied' (Acts 19:6). Receiving the gift of the Holy Spirit is part of the new birth, and unless a person is born again he cannot enter the kingdom of God.
For more on this subject, please read our article titled 'Speaking in Tongues in the Church' found on the Doctrine shelf of the Apostolic Free Library.