I don't know much about the Kievan Rus, and I can't find any good sources about the worship practices of the Rus or much about their mythology. I have found a load of sources for the baptism of the Rus, but nothing about how they worshiped their own pantheon.
Stacey Watson wrote an article on "Vladimir's pantheon", which is a reference to Vladimir the Great's reform of the Slavic paganist practices by unifying them into one central cult that worshiped a pantheon of seven deities (some call this a six-deity pantheon, as Veles was separated from the others (see below)). In short:
Perun: The god of the sky, thunder and war. Most of the statues were made of oak or stone and, in Perun’s case, oak was the most common material used to create his statues. Many villages would carve his statue on the most note-worthy oak tree in the area.
Dazhbog: The giver god.
Stribog: The son of Perun and god of winds, air and sky.
Simargl/Semargl: The god of fire and fertility.
Mokosh: The goddess of fate and the protector of women in childbirth. She also watched over the weaving and spinning.
Khors: The god of the solar disk.
Veles: King of the underworld, harvests and cattle. Veles was separated from the other deities of the pantheon for some reason. As such, he had a separate cultic center a the bottom of the Kievan hills.
Watson also mentions a pre-Vladimiric deity:
Rod: The creator of all things that exist, including the other gods, which makes him technically the supreme Slavic god.
According to Wikipedia, Rod was worshiped with offerings of bread, porridge, cheese and mead. He also had a manifestation of the microcosm of kinship called Domovoi/Domovoy, the god of the household and kinship ancestry. Domovoi sometimes had a female counterpart called Domania, goddess of the household. According to Wikipedia:
"Sacrifices in honour of the Domovoy are practised to make him participate in the life of the kin, and to appease and reconcile him in the case of anger. These include the offering of what is left of the evening meal, or, in cases of great anger, the sacrifice of a cock at midnight and the sprinkling of the nooks and corners of the common hall or the courtyard with the animal's blood. Otherwise, a slice of bread strewn with salt and wrapped in a white cloth is offered in the hall or in the courtyard while the members of the kin bow towards the four directions reciting prayers to the Domovoy."
According to the Encyclopedia of Ukraine, the Rus at a time had a ruling god named Troian, who seems to have been the father of Khors, Perun and Veles. Sometimes Troian was identified with Svarog, god of celestial fire and blacksmithing (source 1, source 2).
Other pagan practices are mentioned in the essay Principal Aspects and Problems of Theology in Kievan Rus' by Gerhard Podskalasky and Gerald Chapple (available now on JSTOR):
"In the canonical questions and answers of the Novgorod deacon Kirik (b. 1110) Bishop Nifont threatened with a powerful "woe [unto you]!" both the offerings of food to the nature gods Rod and Rozhanitsa and the violators of their prohibitions. Regarding the blessing of the funeral feast - whose pagan origin led to its radical suppression in the West...On the other hand, six weeks' penance awaited women who took their children to the "Varangian" (i.e. Latin) priest or the pagan magician to be blessed...Another sermon "on the true faith" describes and condemns...the frequent occurence of dvoeverie among the neophytes who retained their faith in the pagan pantheon after being baptized...as expressed - especeially at weddings - in games, songs, dances, and sacrifices to idols..." (pg. 6-8)
According to Petro P. Tolochko in Religious Sites in Kiev During the Reign of Volodimer Sviatoslavich (available at JSTOR), Vladimir built a temple for the six central deities of his pantheon in the Kievan hills. It was comprised of:
"a stone shrine made of slabs of sandstone mixed with clay and had an ellipsoid shape. Four-cornered projections emerging from the four sides of the temple were oriented to the four points of the compass." (pg. 1-2)
Another structure was found beneath Kiev itself:
"Trenches had ben dug beneath [3 Volodymyrs'ka Street] in the loess to a depth of 60 to 90 centimeters. The trenches were filled with large stones, broken pieces of thin, large bricks, pieces of slate, fractions of lime-water with admixtures of ground-brick, and other materials...The plan was an elongated rectangle...Projecting from the rectangle's northern, southern, and eastern sides were six rounded symmetrical projections shaped like flower petals...They could well be the remains of the temple that is mentioned in the chronicle entries for 945-980. The six petal-shaped projections could have served as pedestals for the idols of the six Slavic gods, namely, Perun, Khors, Dazhboh, Stryboh, Symarhl, and Mokoshka. This is supported by the discovery of a large ashpit located in a cup-like dperession...it contained layers of coals and ash, burnt clay, and a large quantity of animal bones, mostly of bulls. A study of the stratigraphy of the ashpit confirms that it was formed by the burning of a ritual fire. This finding fits in well with the Hustyn' Chronicle, which reports that an eternal fire was maintained beside the temple of Perun." (pg. 2-3)