Special Use Airspace surrounds areas that may contain hazards to flight, or where flight may pose a hazard to other activities. Details about these areas can be found along the edges of the applicable charts, including altitude limits, times of use, and the facility to contact for details (if applicable).
The following are not the only types of SUA. See the AIM for more details on different types of SUA. The images on the right show the examples from the Chart Users' Guide as well as some local examples from ZSE.
Prohibited Areas
It's right in the name. Flight is prohibited. There are exceptions, but if you have to ask about that, then they probably don't apply to you.
Restricted Areas
It's like a prohibited area, but less... restricted. Aircraft can only enter with authorization from ATC, which is typically only when the area is not "active" with the hazards.
Warning Area
Activity here "may be hazardous." No authorization is required to enter, but ATC may advise pilots whether the area is active or not. They start at least 3 miles offshore from the coast and are often extensive. They may be used for anything from flight test activity to live fire military exercises.
Military Operations Areas
Like a warning area, but with more cool planes. These areas may contain a high volume of military activity. ATC may advise whether the area is active. VFR pilots should exercise extreme caution. The chart will list the floor of the airspace: by default it extends to (but does not include) FL180 unless otherwise defined. MOAs are often quite large, but not always.
Alert Areas
Areas that may contain a high volume of pilot training or an unusual type of aerial activity. ATC doesn't generally have any special information or control about these areas. Pilots should be... alert.