Captain America was created during World War II, using the "Super Soldier" Formula, then being bombarded with Vita Rays. This formula effectively turned Steve Rogers into the perfect human, with abilities beyond those of the best Olympic athlete including Enhanced Strength, Agility and reflexes. However, he does not have "super powers" per se; he has the best strength, agility and reflexes that any human can have without being considered superhuman. His immune system allows him to resist most diseases as well as gives him incredible endurance. For example, his metabolism operates at a rate of 4X the normal human; as a result, his muscles build up lactic acid at an extremely slow rate, allowing him to have almost limitless endurance and operate at peak performance for far longer than any conventional human being. Additionally, the Super Soldier serum has effectively been metabolized into Rogers' body; it is that enhancement that somehow allowed him to be frozen in ice in suspended animation for decades (as opposed to dying from hypothermia) until rescued by the The Avengers. The film version of the treatment also gives him heightened mental acuity; he is able to accurately memorize a map of HYDRA bases after only a few seconds of looking at it during a raid.
This movie version uses more the abilities of the "Ultimate" universe Captain America. In which he is super strong and agile, but not to the extent of Spider-man and nowhere near Hulk or Thor. This is demonstrated in the movie when he is easily lifting a motorcycle while three women sit on it for an extended time. That should be between 800 and 900 hundred pounds. Olympic class power lifters can lift around 3.5 times their body weight, with a great amount of exertion. That means a non superhuman Captain America, at peak performance could only lift around 800 pounds under optimal conditions and with a great deal of exertion. If he didn't have some superhuman ability, the movie version could never do this, unless he had some amount of super strength, even with an enhanced metabolism. Perhaps the motorcycle was just fake, made of very light material as a tool to allow the girls to sit on it, and Rogers had to lift barely more than them (which would have constitued an acceptable weight of around 160 kilos). In addition, he is able to leap over a ~10 foot fence while running, clearing it easily. Finally, as his metabolism expells toxic substances very quickly, he can't get drunk.
He was trained in nearly every form of unarmed combat as well as gymnastics; as a result he is considered the finest unarmed combatant in the world. He is so formidable that in a recent story when a villain temporarily neutralized Cap's physical enhancements, he took on four guards escorting him who themselves were enhanced with the same treatment and defeats them all within seconds. He also studied military history and strategy extensively, which will establish him as the ideal field leader of his superpowered fellows in the Avengers. He also has his iconic Shield, which is made of a combination of Vibranium and an unnamed metal alloy; although the alloy has been mistakenly identified as Adamantium, Dr. Myron MacClain (the scientist who designed the shield) did not discover Adamantium until years later. The shield is virtually indestructible; additionally, the Vibranium allows the shield to absorb an extreme amount of impact without transferring it through the shield, i.e. Cap gets punched by Hulk and blocks with the shield, he doesn't get a broken arm from the impact. He uses it as a shield, a blunt object, and throws it like a discus which can be angled to ricochet back to him after connecting with its target, or caroming off other objects before hitting its target.