Permits are issued in the Permit Center. No drawn plans are necessary to get a permit to do mechanical work. You will be expected to briefly describe the work proposed, such as, what sort of appliance you intend to install, whether you will be installing a new vent, new ductwork, etc. The inspector will check the label on the stove or stove-insert at the time of inspection. Fees are based on the number of appliances or chimneys or vents that will be installed.
Gas piping, regardless of the length or number of outlets, requires an additional fee.
As the owner of a single family house or duplex, you can hire a licensed building or mechanical contractor to do the work. OR, you can do it yourself. But that means you- not a friend, neighbor, tenant, or relative. A licensed plumbing contractor may legally install natural gas piping.