Ilúvatarism- The worship of Eru Ilúvatar is the religion of the 'good' peoples of Middle-earth. The specifics of this Monotheistic religion is largely unknown and unspecified by Tolkien, as there is no mention of temples or holy men. An altar to Ilúvatar was atop Meneltarma in Númenor but was for the most part secluded with no buildings or shines. Any additional religious sites are never mentioned and it is unknown if they exist or what they look like.
Melkorism- The Worship of Melkor is also not elaborated much by Tolkien, but if the worship of Melkor by the Númenóreans are any indication, than Melkorism has apart of its service human sacrifice. The Temple to Melkor in Númenor was described as being domed with a hole in the top to allow smoke from the fire below to exit as wood and human sacrifices are burned. The humans under the domain of the Enemy worship Melkor as God, denying the existence of Eru Ilúvatar, Sauron told the Númenóreans that Ilúvatar is a lie told by the Valar to keep the Númenóreans from power. Sauron, since the downfall of Melkor has had himself worshiped as a god by his subjects, it is unknown if other dark entities such as the Witch-king of Angmar are also worshiped as deities in Melkorism.