You take make an image, containing a secret, or something that you'd like us to know anonymously, and upload it. This image shouldn't have your name on it: nothing to tell that it's you.
You can also submit text secrets this time, because of the new system.
Kim tried this before, and others many times since.
I believe the last attempt at this was done in 2008, via photobucket, long before tumblr hit the internets in its current iteration. So this time, we're using that anonymous ask system to support the process of submission. Only I have access to the tumblr account, so there's no risk of the system being compromised like in the past.
You cannot make anonymous image submissions while logged in, but you can while logged out of Tumblr.
The blog is at http://codexsecret.tumblr.com, and is password protected (dontlookhydrogen).
I populated it with the images from the last few rounds that had not been removed, so you can flick through those to get the idea.