I should say something about the Citizens United case, and campaign finance, but I haven't found the time to read the decision yet, and so I don't want to comment to directly about the Court's logic.
As far as the effects, just read what Seth Masket has to say. Long term, most of us think that corporate money is going to find an outlet, so what campaign finance regulations mostly do is affect how, and not whether, corporate money gets into politics. That said, the "how" can matter, and in the short term, disruptions in the rules tend to have unpredictable effects as some players learn to game the system quicker than others, or game the transition in the system while others don't. So the response that this decision will mean that corporations will henceforth run the country after being shunted to the side under the previous regime is wrong, but that doesn't mean there won't be effects, especially in the short term.
When it comes to reform, I like what Seth says, but my ideal reform would be somewhat different I think. I'm in favor of floors, not ceilings. That is, I'd like to see public financing for federal candidates that insures that every House district and every Senate district gets at least a minimally competitive alternative, but after that, I'm of the general opinion that raising money is a fair test of candidate appeal, and I don't mind at all if the candidates who are better at it have an electoral advantage. Oddly enough, that was basically the system that prevailed, although not by design, for presidential general elections from roughly 1992 through 2004, and I thought it worked pretty well. There are lots of reasons that floors, not ceilings is a tough policy to pass through Congress, but I think it would work well in practice and comports well with my preferred version of democracy.