Sometimes people write to me with questions related to kidney exchange, on aspects of which I've written many blog posts. For someone who is looking for a living donor, kidney exchange means that the donor you find needn't be compatible with you, he or she simply needs to be healthy enough to donate a kidney, and willing to donate one so that you get one. One of the several kidney exchange networks can take it from there; it is probably best to work with the one that your transplant center has the easiest working relations with, although you can find the links to the ones I work with the most as you sort through my posts.
When I write to someone who already has a donor I write more than this about kidney exchange, but if you don't have a donor, you need to think about how to get one.
If you are not already registered on the deceased donor waiting list, talk to your docs about getting on the list, since time on the list plays an important role for kidneys. But the waiting lists are organized by region, and the wait is much longer in some regions of the country than in others. (That's why Steve Jobs, who lived in California, got a liver transplant in Tennessee.)
A new organization that helps people register on the waiting lists of regions where the wait is shorter (even if that isn't where the patient lives) is OrganJet (which I've blogged about here). They are mostly involved in helping arrange transportation (since you have to be able to travel for checkups etc. at the distant hospital at which you are registered in addition to your local hospital). But their website has an app that identifies transplant centers with shorter waiting times, and that might be a good way to start, since this is a case in which there may be a conflict of interest between you and your local transplant center.
But a living donor is likely better as well as quicker, if you can find one. Here's a link suggesting how to organize a campaign for a living donor:
Living Kidney Donor Network founded by Harvey Mysel.
There are various kinds of kidney matchmaking sites, like matchingdonors.com, and more specialized sites like http://www.kidneymitzvah.com/ and Renewal.
My impression is that quite a few donors come from faith based organizations, so if you are a member of some kind of congregation, you might let them know of your search for a donor.
There are other options that I don't recommend, but here's a post with a link to an article by the Harvard Law professor Glenn Cohen that seeks to shed some light on overseas markets for kidneys, some less black than others.
(There's a legal market for kidneys in Iran, but I believe you have to be an Iranian citizen to participate in it.)