Look on a tax bill or on property ownership documents. City and county tax assessors usually place a property's parcel number on the property tax bill. You can also find parcel number on the deed to a property, and sometimes parcel numbers are also placed on mortgage documents to identify the property purchased.
Ask a real estate agent. The database that real estate agents use to track available properties for sale uses parcel numbers as one of the identifying numbers. Call the agent you used to purchase your home, or contact a nearby real estate agency and ask the staff if you can search the MLS homes database for your area. Some real estate agencies allow database searches directly from their web site.
Contact your local tax assessor's office. City and county tax assessors maintain parcel maps that the public can search by visiting the assessor's office. Although all assessors keep hard copies of parcel maps for any given area, many tax assessors have begun putting parcel maps online to make searching for parcel numbers easier.