The simplest answer to that question is that the baptism of the Holy Spirit is the receiving of the Holy Spirit. The baptism is the Holy Spirit quickening us, living in us, being Christ’s representation here on earth. Christ has gone away, but He said in the upper room, “I will come again,” and He comes by the Holy Spirit who indwells us and enables us to grow in grace and to persevere in the faith.
I don’t think of the baptism of the Spirit as a post-conversion experience, accompanied by gifts of prophecy or tongues. I don’t think that the baptism of the Spirit is something post-conversion that gives you, say, assurance. I think the baptism of the Spirit is the indwelling of the Spirit at the time of regeneration and rebirth.