Both sides have used various historical maps, treaties, and records (letters, logs, and newspaper articles) to lay claim. The map arguments consist of "hey, I (China) saw it first" and "hey, you (China) called this mine (Japanese) on your map". The treaty disputes involve the Chinese defeat in the Sino-Japanese War, the Japanese territorial loss at the end of WW2, and the return of the islands to Japan from US administration. The islands have been referenced by Chinese officials and newspapers as belonging to Japan, but they were also gifted by the Chinese to a Chinese herbalist and they were in use by Taiwanese fishermen.

http://www.mofa.go.jp/region/asia-paci/senkaku/qa_1010.html#q1

http://www.ioc.u-tokyo.ac.jp/~worldjpn/documents/texts/docs/19710617.T1E.html

http://www-ibru.dur.ac.uk/resources/docs/senkaku.html

http://www1.american.edu/TED/ice/DIAOYU.HTM

I kept my descriptions vague because there are disputes regarding the disputes, such as who owned what during each treaty, and whether or not the islands were considered as a part of other territories. Also, if I can find the paper I wrote on the subject after work, I'll post it here. Edit: Sorry, the paper was wiped when I formatted my laptop.

The basis of the Chinese claim is that the islands appeared on Chinese maps from the 15th century. In those, they are marked as Chinese territory. According to this, they have been Chinese territory since, even if at times they have been illegally occupied by others.

The basis of the Japanese claims is that they found the uninhabited islands in 1884, settled them and controlled them until they lost WW2, when the US took control.

The US controlled the islands until 1971, when they gave control to Japan, with the 1971 Okinawa Reversion Agreement. Japan has been in de facto control since then.