Although directors Joe and Anthony Russo are best known for TV comedies, there's little that's not cinematic about Captain America: the Winter Soldier...save, perhaps, the inevitable knowledge that this movie is but one episode in a continuum that aims to keep going, non-stop, for as long as possible, just like a network series. But that just makes it an accurate adaptation of a Marvel comic, where most larger "event" stories require you to stay up on the ongoing exploits of multiple heroes.
In any case, while it helps to already know who Black Widow (Scarlett Johansson) and Nick Fury (Sanuel L. Jackson) are, and to have seen the first Captain America for background on Steve Rogers (Chris Evans) and a couple of his old acquaintances who resurface, it's not that necessary. The film catches you up in ways that thankfully aren't heinously redundant (Cap visits a museum exhibit based on his own WWII exploits, and that part covers most of it) before doing what it must do...go about the business of being a kick-ass Captain America movie. Which it is.
The timing may be off, geopolitically speaking, for a movie that metaphorically deals with the complexity of the War on Terror versus the clarity of the Cold War - in a coincidence of timing, the movie ends with major characters heading to Ukraine - but so be it. After the morally black and white struggles leading teams against evil Nazis and invading Chitauri, Captain America now finds himself leading missions for SHIELD, many of them covert, some of them morally questionable, and plenty where he doesn't even know the orders his other teammates have that may conflict with his own. Regardless, he gets in plenty of the shield-slinging you've always wanted to see him do, facing off against lesser villains like mercenary Batroc (Georges St.Pierre).
When he tries to question Fury about the morality of his actions, and why more intel isn't being shared with him, he mostly gets met with Sam Jackson quips like: "I do share. I'm nice like that." But when Fury is targeted for assassination by what appear to be corrupt cops and the mysterious masked super-villain Winter Soldier (Sebastian Stan), Cap must take orders from the even more morally questionable Alexander Pierce (Robert Redford) and soon finds himself on the run, unable to trust anyone beyond his fellow Avenger and SHIELD teammate Black Widow, and his occasional jogging buddy Sam Wilson (Anthony Mackie), whose Falcon persona here is simply "guy who has access to high-tech equipment" rather than anything Red Skull-related.
Despite the Disney publicity machine's own apparent attempts to spoil more than that via all the clips they've been releasing, it's best not to reveal many more details beyond that. Marvel wants to lure older moviegoers in by comparing this to '70s political thrillers, while neglecting the crucial point that part of the appeal of those thrillers was that the hero could sometimes lose, fail and even be dead in a ditch by the end, and it's surely no major spoiler to say that won't happen to Captain America. As Thor: The Dark World showed us, Marvel will sometimes make you think drastic developments in their cinematic universe have happened only to walk them back later - there's some of that here too, but there are also significant changes to the larger continuity that will have ripple effects, especially on the Agents of SHIELD TV show.