The vent pipes are part of the drain-waste-vent, or DWV, system of a house or building, and they do not carry water inside them. Instead, they serve to equalize air pressure within the DWV system, and also release sewer gases into the outdoor air, as all vent pipes terminate through the roof. When a clog occurs in a vent pipe, you normally climb atop the roof to attack it, but you can also try to clear it out from within the house.
Look up on the roof, from the ground below, and locate the vent pipe's position. The top of the vent pipe extends through the roof.
Climb into the attic, and locate the vent pipe, as it passes through the attic.
Cut out a section of the vent pipe, using a hacksaw.
Insert the end of an auger cable into the pipe. An auger is commonly called a plumbing snake, because of its flexible cable that snakes through piping. Crank the auger handle clockwise, to extend the cable through the pipe so that it reaches and breaks up the clog. Crank the handle counterclockwise to retract the cable once you have cleared out the clog. Do this downward and upward in the vent pipe, if necessary.
Measure the gap that now needs to be closed within the open vent pipe. Use a tape measure to measure from end to end of the open pipe area. Also, measure the pipe diameter, using the tape measure, if you do not already know it.
Scrape the ends of the pipe with a utility knife to remove all the burrs from it.
Apply PVC glue to both open ends of the vent pipe, and also to both ends of a PVC coupling. Make sure you have a coupling that is the same diameter as the vent pipe, and is also the right length to seal the open distance.
Install the coupling into position within the vent pipe.