Depends on the airline. Usually regionals will allow you to jumpseat/non-rev on company airplanes within a couple weeks (once your background check clears). Non-rev privileges on mainline partners may take 30+ days.

You can list at the ticket counter or even the gate, but normally you list via a phone number (some automated, some not). Some companies have websites that show loads and/or allow you to list yourself online.

In order to get your immediate family members signed up you will need birth certificates and/or marriage licenses.

Some airlines don't charge for non-rev, others charge an anual fee ($50-80), others charge a small mileage fee (UAL). The mileage fee can add up if your weejly commute is a long one.

Also sometimes the fees for your family members may get deducted from YOUR paycheck. If possible, ask them to pay the fees at the airport. Parents usually have to pay taxes for each leg, so they end up getting charged more than you and your spouse/kids.