A circling approach is conducted when you gain visual reference and can not make a normal descent to land on the chosen runway from your current position.
In a nutshell, when circling to land, you fly the traffic pattern as much as possible, and remain at or above the circling MDA until you are continuously in a position from which a descent to land can be made at normal descent rates and with normal maneuvers. Depending on the position of the landing runway and the aircraft, the exact maneuver will vary, generally it is the shortest path from the current position to the downwind or base leg of the landing runway. The pattern can be either left or right at the pilot's discretion, though a control tower will often specify how they want you to circle.
Circling minimums vary according to the approach type and terrain/obstacle considerations. Circling minimums are usually higher than straight-in minimums.
There is no speed limit specifically for circling approaches, just the usual airspace speed limits, 250 knots below 10,000 MSL and 200 knots within 4 miles of the primary airport of class C or D airspace below 2,500 AGL.
There are category speed limits which define various minimums for the approach. The speed at which you fly the circling maneuver defines the minimums required, they vary for each approach, and may be the same for each category. Example: less than 91 knots is category A, 91-120 knots is category B, 121-140 is category C, 141-165 is category D, 166 or greater is category E. Contrary to what many people believe, the category you use depends on the speed you are currently
flying. This means that if you are bombing along in your C172 at 141 knots, you must use the category D minimums, even though approaches are usually flown at 90 knots.
Circle to land is used whenever the chosen approach does not put you in a position from which you can execute a straight in landing on the chosen runway. Many non-precision approaches have the missed approach point right over the center of the airport. If you break out there, you're not going to be able to land straight in on any runway and must circle. Some approaches are not aligned with any runway at all, and only have circling minimums. However, if you break out early enough, you can enter into a straight in approach on a runway.
Hope that made some sense.