What exactly was Hitler's plan for victory in the Soviet Union?

In very general terms the "plan" was to quickly defeat the Soviet armies in the west during the summer months of 1941, occupy the main centers of population and industry in the western Soviet Union and then push east against, presumably, relatively light resistance. The military end goal of operation Barbarossa as such was the so called A-A-line, basically a line from the arctic port of Arhangelsk to the Caspian Sea port of Arstrakhan. It would have provided a natural border along the Volga river.

This plan called Operation draft East is the foundation for what would later become Fuhrer directive 21, aka Operation Barbarossa. It was the brainchild of General Erich Marcks, a WW1 veteran The actual direction of Operation Barbarossa, the northward thrust towards Moscow and southern thrust towards the caucasus oil fields, were dictated in large part by the so called Lossberg study which advocated a main thrust north towards the Pripet marshlands.

Was he under the impression that taking Moscow would be all that was needed for surrender?

I would hazard to say that Hitler and the OKW were very much aware of the possibility of Stalin not surrendering even if all of western Soviet Union was lost, despite what he may have said in firey radio adresses. He made several remarks about Stalin fighting from Siberia, however, he equated it to him trying to reconquer Germany were he to be pushed back into Slovakia meaning roughly that he didn't think it much of a threat. Western Russia contains and contained the vast majority of Soviet industry and population and what industrial centers there were further east were to be targeted for strategic bombing by an air fleet.

Did he actually think that the German army could logistically support supply lines 5k miles away, and they could drive all the way east?

No but nor did the ever plan to. The goal was, initially, to have Japan push west through Siberia, dividing Russia in two at the Ural mountains which wera and still are considered the natural border between Asia and Europe. Later on the plan was revised so that Russia was to be divided at the Yenisei river. The largely rural and sparsely populated lands to the east were envisioned as mostly agricultural vassal states likened to the British colony of India but geographically more closely tied to Germany. These plans were of course never very concrete because we all know what happened in the East but I hope it answers your questions.