I don't think I could give you a comprehensive answer to this question in a short space. Hare Krishnas, as you have labeled them, are members of the International Society for Krishna Consciuosness (Iskcon). It is a mission established by A.C. Bhaktivedanta Swami to spread the teaching of Gaudiya Vaishnavism globally. My teacher is a student of A.C. Bhaktivedanta Swami's but has established his own mission independent of Iskcon. Vaishnavism and Saivism are the two major branches within the Hindu pantheon, but by no means are they the only lineages.
I could give you more details on the basic beliefs of the Hare Krishnas but it would be much more informative for you to read the Bhagavad-Gita commentary written by A.C. Bhaktivendanta Swami as it will give you a comprehensive and detailed answer to the question regarding belief.
Yours in service,
Audarya-lila dasa
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