Originally Posted by cherokeesam
Cap had extensive military training when he joined the Super Soldier program. Conceivably more than your average GI. And that was when he was still a 98-pound weakling. Then he had about 2.5 years of real-time combat experience in the biggest war the world has ever known; and the fact that he spends a lot of time in the gym indicates he's always training and staying in shape.
Of all the MCU superheroes shown thus far, Cap is the one with the best resume when it comes to combat and small unit tactics. Natasha might arguably have better martial arts skills than him, but his super-'roids means that he could beat her to a pulp.
TL/DR: Cap don't need no more training. He's already a Super Soldier. Keyword: soldier.
I'm just going by what we see on screen. He had no more than a few days training before the serum was injected into him. From there, he became a propaganda tool, before breaking away and relying on his natural talents to become the "proper" captain america. From there, he got his shield and went about destroying red skull's facilities. I don't see where he got any martial arts training in, in that time. If he did get some, we didn't see him use any in the first avenger. Then he gets frozen and wakes up and i think the avengers takes place shortly after the end of TFA, so he hardly could have gotten proficient in any martial arts; assuming he even started training in them.
Cap's hand to hand abilities are what make him such a threat despite not technically having super powers. From where I stand, it is this aspect of his character that has been largely ignored in the two films he has been in. I am hoping he trains in shield hand-to-hand or something like that in the interim between the avengers and the winter soldier. It would be a nice change of pace from the other marvel movies to have a straight up martial arts fight.