In regards to super PACs, this is a nice overview.
Some key points:
- there is no donation limit. Anyone or any corporation can give any amount.
- there is no need to disclose contributors. Since a contributor can be a corporation, and a corporation doesn't need to reveal any specific individuals, an individual can contribute unlimited funds via a corporation and not be directly exposed. (Stephen Colbert does a nice explanation here: http://www.cc.com/video-clips/3yzu4u/the-colbert-report-colbert-super-pac---trevor-potter---stephen-s-shell-corporation where he shows how a candidate can anonymously funnel money into "their own" SuperPAC)
- the key limits for spending are that the Super PAC can't contribute directly to the candidate's campaign, nor can it coordinate with said campaign (though it's generally assumed that coordination happens when needed via loopholes).
The most debated issue is what happens to the money after the campaign. The law is actually fuzzy there and some claim that a candidate can simply pocket the money after they drop out or the election is over. Stephen Colbert, again, did a really nice explanation on his show as to how one can easily funnel all the money from the PAC into one's personal account (in this case, $800,000):
Citizens United is explained quite thoroughly only Wikipedia. In the context of this question, it allowed for the formation of the aforementioned Super PACs.