A close-up lens (diopter) reduces the effective focal length of the lens it is attached to. Because of that it decreases both the minimum focus distance and the maximum focus distance. When the main lens (also called the prime lens, 'prime lens' having two different meanings) is set to focus at infinity, the combination will be focused at the focal length of the close-up lens. For example, a 3 diopter close-up lens has a focal length of 1/3 metres, so when the main lens is set at infinity, the combination will be focussed at 1/3 metre.
The reduction in focal length does mean that working distances are reduced when compared to extension tubes with the same main/prime lens at the same magnification.
If you take a 50 mm prime lens and a 3 diopter close-up lens, the combination will behave like a 43 mm lens. A 50 mm lens is a 1000/50 = 20 diopter lens, so the combination is 23 diopters, or 1/23 metres, or 43 mm.
There is usually no need to make an adjustment to the f-number.
Close-up filters are of varying quality. There are simple single-element lenses and double or triple element achromats (ie they have some correction for chromatic abberation). Leica, Nikon and Canon, among others, make achromats. Nikon and canon also make single element lenses. Within Nikon's range, the 'T' designation usually means that it is the higher quality version, eg the 4T.
Best,
Helen