The period your looking for is called 'Kofun' (300-593 ad).
People lived in clans (the head of the clan was both their worldly and spiritual leader and each clan had their own deity),
burial culture evolved (the graves became above-ground structures (mostly shapes like keyholes, rather funny)),
the three national symbols of Japan (the mirror, the sword and the magatama (an ornamental sword with jewels, no one knows the real purpuse of it) became burial gifts (they were already religious symbols in the Yayoi period, the one just before Kofun),
Shinto (the Japanese religion) took shape,
they had contacts with China (trade mainly and they paid tribute to the Chinese emperor) , they copied the Chinese writing system (called 'kanji', the Japanese later modified it, since there are a lot of differences between Chinese and Japanese (the latter one has gramatical endings, the first one not)),
confucianism was introduced, and in 538 or 552, boeddhism was introduced (from Korea, the Yamato had good contacts with the Korean province Paekche).
The Yamato were the most powerful clan, their clandeity (the sungoddess Amaterasu Omikami became (and still is) the upper-goddess in Shinto. They also became the 'Emperors' family' (every emperor of Japan is decendant from the Yamato)
Hope this helped a bit
, if there are any problems, feel free to ask.
Medieval Japan?
