There are three main methods for ligating vector and passenger DNA: 1) Sticky or cohesive end ligation joins DNA fragments with complementary overhanging ends using DNA ligase. 2) Blunt end ligation relies on T4 DNA ligase to join blunt ended fragments, which are then given sticky ends using restriction enzymes. 3) Homopolymer tailing adds complementary homopolymer sequences like oligo(dA) and oligo(dT) to the 3' ends of DNA molecules to enable their ligation.