Tatami room is the most common thing which Japanese classic houses have. There are couple of manners for living with Tatami room.
Japanese houses have separated by shoji(paper window) or fusuma (paper gate), and this represents the territories of house owner. Stepping on doorsill directly means dishonoring the owner of the house because you are not respected the territories. Japanese say "Stepping on doorsill is like stepping owners face." Also, if you step on the doorsill, it will damage the house structure.
There are several origins. One of the main reason was coming from Samurai's self-protection. Old time, some of assassins stayed under Tatami, and stab sword from the edge. Also, Tatami was used to be very expensive furniture, and on the edge of Tatami, it had "Kamon" family symbols. It was very dishonoring to step on house owners Kamon.
Instead of knocking, use light cough and say "Shitsurei shimasu(excuse me)." Use only one hand to open Fusuma. Using both hands is lazy manner. At right siding Fusuma, put right hand on pull-tab to open about 10cm (3 inches) and put the other hand on the side edge of Fusuma to open wide enough to enter. Then, use pull-tab to close. Say "Hi," after you completely finish entering.