Different methods of water main repair include traditional trenching, where the damaged section is excavated and replaced, and trenchless methods like pipe bursting, where a new pipe is pulled through the old one, and pipe lining, which involves inserting a resin-coated liner that hardens to form a new pipe inside the old one. Trenchless techniques are less invasive, causing minimal disruption to the landscape and infrastructure, while traditional methods may be necessary for severe damage.