This post is for beginner photographers out there who are interested in getting started to experiment with long shutter speeds for landscape or any other photography. The question answered in this post is "How do I get long shutter speeds?". This post do not answer questions such as "When to use long shutter speeds?". However, there are a few different ways to achieve long shutter speeds and they are explained below.
The smaller aparture you use the longer the shutter speed will be. Note that a higher number indicates a smaller aparture. Depending on your equipment the smallest possible aparture might vary but it is usually something likge f/22.
Use as low number ISO as possible, usually 100 or 50 is the lowest setting on digital cameras. Shutter speed will be twice as long using ISO100 instead of ISO200 and four times as long instead of using ISO400.
An ND filter is a grey tone filter that you put in front of your camera lense in order to letting less light through the lense to achieve longer shutter speeds. ND filters come of different densities graded ND2, ND4, ND8, ND16, ND32, ND64 and so on where ND2 is the brightest.
If possible you can try to shoot the subject in darker conditions. If you for example want to shoot a landscape scene with long shutterspeed do not shoot it during the brightest hours (of course there are thousand of other reasons not to shoot a landscape scene during the brightest hours).
I would not recommend overexposuring a photo in order to achieve a longer shutter speed but it is fully possible. If you do this I recommend you shooting RAW and keeping an eye on the histogram to make sure the whites still are not burned.
Please note that in most cases it is strongly recommended to use a tripod when shooting with long shutter speeds even if there are a few exceptions to this recommendation.