The Holy Spirit is God - and when we come to Christ and give our lives to Him, God comes to live within us by His Spirit.
In other words, if you are a Christian - if you honestly have asked Christ to forgive your sins and have opened your heart and life to Him - then the Holy Spirit already lives within you. You don't need to beg Him to enter your life; He is already there (whether you feel His presence or not). The Bible says, "If anyone does not have the Spirit of Christ, he does not belong to Christ" (Romans 8:9).
In fact, before you committed your life to Jesus the Holy Spirit was already at work, convicting you of your sins and convincing you that Christ can save you. He did this because God loves you and wants you to be with Him in heaven. If God didn't care about you He wouldn't do this - but He does love you, and He sent His Spirit to draw you to Christ. Jesus said, "No one can come to me unless the Father who sent me draws him" (John 6:44).
But the Holy Spirit's work doesn't end there. God wants you to become more like Christ - and this is only possible as we yield our lives to the Holy Spirit and ask Him to change us from within. We don't have the power in ourselves to transform our lives - but God gives us the power, as we submit to His Spirit every day. Is this happening in your life?