How a presidential TFR is shaped
The usual VIP restriction is two circles around the place being visited, from the surface up to just below 18,000 feet. The inner core, typically 10 nautical miles in radius, is closed to almost everyone: scheduled airlines, military, law enforcement and approved medical flights are the main exceptions. The outer ring, typically out to 30 nautical miles, is open to aircraft that file a flight plan, talk to air traffic control and squawk the code they are given.
Inside the whole area, training flights, aerobatics, gliders, parachuting, ultralights, banner towing, balloons and drones are normally not allowed. The exact shape, times and exceptions are in each notice, and they differ from visit to visit.
Drones
Recreational and commercial drones are prohibited inside a VIP TFR unless the operator has specific approval. This applies even to small drones flown low over your own yard. Check before flying when a visit is announced near you.
For pilots
VIP restrictions are issued under 14 CFR 91.141 and 99.7. Read the full NOTAM text, not only the map: start and end times move, and a single visit is often published as several notices for different days. Aircraft that stray in can be intercepted, and pilots face certificate action and fines.
Why the times keep changing
Schedules for these visits shift, so the FAA amends or cancels the notices, sometimes hours before they start. This page reads the current list every few minutes. See every restriction, including stadiums, wildfires and launches, on the TFR page, and how notices work in What a NOTAM is.