The price will vary depending on the breeder and the lines of the dog. More reputable breeders who breed champion dogs will charge in the thousands, whereas backyard breeders will charge in the hundreds; some backyard breeders will get desperate when they have trouble selling and will reduce the price even more. Or you can find a Great Dane to adopt. Champion dogs will cost more, dogs with champion lines will also cost more. Plain Great Danes from backyard breeders may not be of good health or good genetics but they'll be cheaper. Pay for what you get. Adoption is great because you can save a life, get a spay/neutered dog and pay say $200 for everything.
Danes are prone to health problems that can be costly, so keep that in mind as well. Poor genetics and breeding can be more costly in the end, when trying to save a few bucks buying the puppy.
Try looking for breed specific rescues before you look for a breeder. You can find healthy puppies, young, and adult dogs for adoption. You can find pure bred dogs, as well.