Single play dan has 4 songs, double has 3.
There are 3 types of dans, Kyu, Dan, and Kaiden.
Kyu courses are the lowest ranking dans. 7-Kyu is the lowest, with songs of level 1, with songs on Beginner and Normal difficulties...simple enough. The highest is 1-Kyu, with simple level 5 and 6 songs. In doubles, 5-Kyu is the lowest kyu rank course. These courses are colored light green in the game.
Dan courses are the standard level in dan mode. 1-Dan is barely different from 1-Kyu, which is one step below it. 1-Dan contains easy 6s. The default dans are colored blue and range from 1-Dan to 8-Dan. The dans progress a bit more than the kyus do with each step up.
Dans 9 and 10 are colored red and are basically the boss dans. 8-Dan is a mix of hard 10s and easy/mid 11s, while 9-Dan would be tougher 11s. 10-Dan contains 11s and 12s. These dans are unlocked after beating 8-Dan.
Kaiden was introduced in Distorted as basically the god course. It's colored gold in dan mode. This contains all 12s and basically the hardest 12s in the game. It's unlocked after completing 10-Dan. To give an example of how hard this course is, here's the Kaiden course for Distorted CS:
quell [a]
Nageki no ki [a]
Go beyond [a]
Mei [a]
All of those songs are the hardest to pass in the game.
Anyways the dans from lowest to highest would be:
7-Kyu (Single play only), 6-Kyu (Single play only), 5-Kyu, 4-Kyu, 3-Kyu, 2-Kyu, 1-Kyu, 1-Dan, 2-Dan, 3-Dan, 4-Dan, 5-Dan, 6-Dan, 7-Dan, 8-Dan, 9-Dan, 10-Dan, Kaiden.
That should clear it up pretty well.