In the 1940’s, Asian martial arts like Kung Fu and Karate were largely unknown in the west. And if they were known, westerners were often hard-pressed to find teachers. However, Judo and Jujitsu were somewhat popular, especially in America, thanks in large part to Teddy Roosevelt.
So, it is safe to assume that Steve Rogers, as part of Basic Training in the Rebirth Project, would have been exposed to most known forms of hand-to-hand fighting. Most predominantly would probably have been boxing, with a dash of Judo and Jujitsu. And, since we were allies with the French, probably some Savate got mixed in as well (which really meshes with English/American boxing). We’ll talk about the shield later.
As a result, we have a Captain America who fights predominantly with his fists, using a few kicks if the range is right, or his hands are otherwise occupied, and then some basic blocks, joint locks, and throws. None of it would be flashy. It would be a style of economic movement, meant to disable and move on quickly. And since Cap was the only Super Soldier, he would be expected to be engaged solo against multiple foes, so his style would have to account for that as well. Relying on his superior athleticism, he would often simply dodge and weave during a fight.
Cap’s original shield was a variation of the kite shield, and was mainly just for symbolism and show. As a fighting instrument, the kite shield is very effective in blocking direct attacks, and providing a lot of coverage, but because of the unwieldy shape, it had pretty limited offensive capabilities beyond the standard shield-bash (which, in the movie, was a favorite move for Cap).
When the round shield was introduced, some of the overall cover was lost due to a reduced size, but the advantage of different modes of attack, such as striking with the edge in a punching motion, became available. Normally, shields are not thrown. The only feasible reason that Cap started doing so was because of the vibranium construction.
It was stated that vibranium absorbs kinetic energy. However, that energy has to go somewhere. Naturally, the vibranium would just pass it on as a sort of “gust” of dissipated energy. With the shield being made in concentric circles, this energy was bled out to the edges. However, when the energy originates at the edge, the net effect is that the energy is “bounced” straight back. Thus, when the shield would hit something, the energy generated by the object being struck, would bounce back into that object, essentially doubling the force of the impact.
However, without Cap’s considerable strength behind it to force the energy back into the target, a thrown shield would rebound at a relatively equal speed. Through trial and error, and a lot of practice (presumably while the HYDRA base assaults were being planned), Cap is able to master the intricacies of aiming the shield in order to direct the rebounding energy in specific directions, thus enabling him to bounce the shield off of multiple targets, and have it return to him.
In the end, we have a Captain America who punches, kicks, occasionally throws, and often shield-bashes his way through Nazis and HYDRA agents. His fighting style is unique to him, as it relies greatly on his enhanced strength and reflexes. He is able to withstand blows, even through his shield, that lesser men would not (such as Bucky on the train), and is able to make use of unorthodox techniques, like throwing the shield. In short, he is a unique character, that others may emulate, but none may ever fully duplicate.
