The names Giliarovskaia gives are usually accurate and documented for the Muscovite (post-Mongol, ie. after 1450s) period. The Kievan (earlier) period, however, is more of a problem for costumers and linguists alike.
The consensus at this time seems to be that the mid-thigh to knee-length shirt for men, and the undertunic for women, were both called srachitsa, sorochitsa, or sorochka, and that rubakha (the modern word for shirt) corresponded instead to “garment” generically.
The cloak worn over the left shoulder, leaving the sword arm free, was called the korzno, and it was a distinguishing garment of the Rurikid princes. The fur coat, sewn with the fur to the inside and covered with fine cloth on the outside, was called, as it would today, shuba.
Shapka was a man’s hat; kokoshnik, kika, were women’s headdresses (the names may refer to different types of headdresses, but the exact nomenclature appears to vary by region and in time, and these variations seem to have persisted to this day). The veil was called povoi.