Step one is to download a dictionary, if you haven't done that already. The dictionaries are the same kind used by LibreOffice, OpenOffice and others, and can be downloaded from e.g. http://archive.services.openoffice.org/pub/mirror/OpenOffice.org/contrib/dictionaries/ The Danish one is da_DK.zip.
After downloading, unzip the archive, and place it somewhere convenient. It doesn't really matter where you place the files, I think.
To activate the dictionary in Texmaker, go to Options --> Configure Texmaker, and look under the Editor page. In the middle there is a field called Spelling dictionary. Click the folder icon next to it (highlighted in screenshot) to browse for the files you just downloaded and unpacked. Among the downloaded files there is one called da_DK.dic, which is the one you want. Click OK, and you're done.
Updated Dictionary Link
The new working link for acquiring Danish Language can be found on Apache OpenOffice Extensions. Just unpack the .oxt file as an ordinary ZIP file.