Hey Hudson,
I missed this earlier...
Dancingalone is pretty much there, but I'll add a bit.
Koryu literally means "Old School/Flow" (Ko = old, Ryu = school/style/flow). It refers to Japanese systems that have origins predating the Meiji Restoration of 1862. Gendai systems are those that have origins after this date.
These systems can be expansive, covering a large syllabus, or highly specialised, depending on the Ryu-ha itself. There really is no one "model" for Koryu. Some of the most famous include Tenshinsho Den Katori Shinto Ryu, which dates from the 15th Century, and is considered the oldest extant system of swordsmanship in Japan, Takenouchi Ryu, considered the oldest systematised school of Jujutsu, Negishi Ryu, a school focusing on Shuriken, Owari Kan Ryu and Hozoin Ryu Takeda-ha, both teaching spearmanship, Toda-ha Buko Ryu, Yoshin Ryu, Jikishinkage Ryu, and Tendo Ryu who teach Naginata, Araki Ryu and Yagyu Shingan Ryu, teaching a variety of methods, Kashima Shinryu, Hyoho Niten Ichi Ryu, Yagyu Shinkage Ryu, and Jigen Ryu teaching swordsmanship, and much much more. A number of these schools have various branches (such as Araki Ryu, Takenouchi Ryu, Jigen Ryu etc), but others are very definate on a single transmission through a single line (such as Hyoho Niten Ichi Ryu and Katori Shinto Ryu).
In terms of "how do you get it", do you mean how is something classified as a Koryu tradition? Simply, it has origins prior to 1862, and is Japanese. That's about it. However, how you become a member of a Koryu organisation, well that is a different matter. It involves subjecting the Ryu to the organisation in question in order to have them verify the lineage or history, apply to the organisation, and in some cases, pay to be a member (others don't require this). As a note, however, not being a member of an organisation doesn't mean the system isn't a Koryu (I believe the Kashima Shinryu, under Kunii Zen'ya, refused to be a member of a Koryu organisation as he disagreed with some political issues).