Operations in Class B,C,D, and E airspace are allowed with the required ATC permission. Operations in Class G airspace are allowed without ATC permission. Don't fly within 5 miles of an airport unless you contact the airport operator and control tower (if operating at a tower-controlled airport) before flying. Filing a Drone Notice to Airmen (DROTAM), while not required, is a good practice!

The following recording by Sarah Rhodes describes in more detail the different classes of airspace, and how to interpret them on an aeronautical chart.

Flight Restrictions

Flight not allowed during Temporary Flight Restrictions (TFRs) without explicit permission. Times and locations of active TFRs can be found through the following services:

Flight Service at 1-800-WX BRIEF (800-992-7433)
Aloft.ai (do not make an account with a vt.edu email)
www.1800wxbrief.com
tfr.faa.gov/
Real Time TFR Site

Website showing real time TFR updates

No-Fly Zones

The FAA has also designated other no-fly zones including:

National Parks
National Wilderness Areas
Nuclear power plants
Military facilities and bases
NOAA marine sanctuary areas
Prisons
Stadiums and other venues where large crowds are present (e.g., Hokie Football games)
Always check local laws for state and municipal parks for other restrictions