Diagnosis comes first. Lifting the manholes tells the engineer which section is affected: a full upstream chamber and an empty downstream one puts the blockage between them. That takes minutes and saves hours of guesswork.
Rods are used for short runs and soft obstructions. Jetting is used for everything else — a hose is fed down the run and water at 2,000-4,000 psi is directed backwards through the nozzle, pulling the hose along while scouring the pipe wall clean.
The last step matters most: a camera run to confirm the pipe is genuinely clear and to identify any defect that caused the blockage, so you are not calling someone out again in six weeks.