Draw a plan for a new drainpipe showing how it will be vented and where it will connect to the drain-waste-vent system. Have your plan approved by a local plumbing inspector.
A kitchen usually does not have a 4-inch line that requires a thick wet wall as in a bathroom. Kitchen plumbing sometimes runs through an exterior wall, but pipes should be well insulated. In areas with cold winters, run supply pipes up from the basement through the floor rather than through the wall.
Remove all cabinets that are in the way. Completely cover all cabinets and flooring that you will reuse to protect them.
If wiring is in the way, shut off the power to the circuit and test to make sure power is off. You may want to remove a cable before working on the drain.
About a day to run a new drain line with a revent
PVC saw or circular saw, level, layout square, drill with hole saw, reciprocating saw
Cutting and joining PVC pipe, running pipes through walls, connecting new pipe to old
Clear the room of all obstructions; have your plans approved by an inspector
PVC pipe and fittings to suit local codes, PVC primer and cement, fitting for joining to the drainpipe, pipe straps