Orthodox: torah, both written and oral, was given by God at Sinai. This includes the rules to apply the law. Chain of authority is per Avot 1:1. We don't make/revisit law today because that requires the Sanhedrin. (Of course, we do continue to interpret law to account for new situations, but we don't overturn existing law.)
Conservative: torah at Sinai (some say divine inspiration rather than divine authorship); process, authority as above. However, we can derive law today even without the Sanhedrin, and even if it contradicts existing law, to take into account new information. For example, the need for a second day of yom tov comes from calendar uncertainty that we no longer have, so we don't need to keep it. A community follows its rabbi, as for Orthodox, but there can be more variation because the law body supports minority opinions.
Reform: opinions about Sinai vary, ranging from "happened as written" to "some sort of divine encounter that Moshe tried to put in words afterwards" to "literary device/metaphor, didn't happen". The ethical mitzvot are completely binding, per the prophets. Individuals and communities have informed autonomy but are not supposed to pick and choose at whim. There is probably more variety in this movement than the others in what people do and believe.
In all of these I've described what movement leaders hold and teach. When I was shopping for a synagogue, I asked rabbis of each movement what distinguished their movements and this is pretty much what they said. This is the "theory"; the practice of individual Jews can vary (less so in Orthodoxy).