What channels must a developer go through to ask for the rights to a character? I want to make a point and click adventure based on Freddy Krueger, and I know my chances are slim, but how do you even go about asking?
Have your people call their people.
You need to find contact information for the appropriate business/legal department (or person) within the organization that holds the intellectual property rights that you want to license. This can be a single person, in a smaller studio, to an entire department (at a large publisher for example). This may be difficult to do because that information isn't always readily made available on a company's website: you may need to resort to calling reception and asking to be put in contact with the appropriate person, or mining some industry contacts you may have to arrange a meeting.
Note that you can expect a prolonged series of discussions and meetings, during which you will likely need to discussion with the IP holder many of the details of your project, your financials (current and future projections based on your use of the IP) and many other business tidbits. This is a business deal, after all.
If you don't have your own business/legal representative, consider retaining the services of some kind of lawyer for the purposes of brokering the deal. They are likely to be far more knowledgeable than you in the details of IP law and the associated licensing agreements: you are extremely unlikely to get a blanket, informal "sure use our characters" grant of permission from a savvy IP holder. You're more likely to end up negotiating some kind of contract, where they grant you some limited use of their IP in exchange for some combination of money, share, control over your project, et cetera.