Removing a tattoo can be a challenge - which is why you should think very carefully before you get a tattoo in the first place. It costs more and takes a lot longer to remove a tattoo than it is to get one.
How long it takes depends on the size of the tattoo and also the colors - teal and pink are particularly difficult. It can take many sessions (ten to fifteen even for a small black tattoo) over a period of years. Each removal session takes 15 to 45 minutes, depending on the size.
Removal sessions can generally not be scheduled less than six to eight weeks apart. Newer techniques promise that some tattoos may be removed in six treatments or fewer. Even then, complete removal of the tattoo is not a guarantee, especially if you smoke. Often, you are left with a faded mark which may only be visible close-up but is still very definitely present.
Darker colors generally fade faster than lighter ones. Fluorescent tattoos are almost impossible to remove. If you have used "cover art" and then want the entire thing removed, that can take a long time.
So, the answer is: It takes months to years to remove a tattoo unless it's a small black and white one, your dermatologist has the newest equipment, and you get lucky. With each session costing anything from $150 to $500, the take home is to seriously consider that ink in the first place. However, new techniques mean that more and more people are seeing satisfactory results with laser tattoo removal, and the technology continues to improve. Also, there are few side effects from tattoo removal and newer methods are considerably less painful than older techniques.