I see that many people say the easiest way to get a postdoc position (in US) is to come with your own funding. Some postdoc "openings" are only contingent on self-funding. But all the postdoc fellowships I see require a mentor to design a project with, so I'm confused about the process here. Where can you acquire postdoc funding without having a position already?
Generally you would select a few professors whose work you admire and write to them to say you are excited by their work, explain how you would fit in and ask if they would be willing to discuss the possibility of applying for a postdoctoral fellowship with them as the mentor. When you do this it will definately be in your interests if you were to mention specific fellowships you are thinking of applying for. It has been known for well funded professors in the US to offer to fund an exceptional candidate for the first year while they apply for funding, but I wouldn't assume this.
If the professors were positive you would then generally have a discussion about projects that would fit both of your interests. I would guess you would then write the application with their help, and cross your fingers while you waited for a response.