Take a look at advanced settings under the list  settings. You can
easily set this without needing to break security inheritance and setup
custom security.

This isn't working.

In the Advanced Settings for the list, I have Item-Level edit  Access set
to "Only Their Own".

All permissions  are set to "Contribute".

I assume that Edit Access of "Only Their Own" is checking the "Created
By" field?

If so, it's not working. At this point, everyone can edit everyone
else's items.

Ideas?

Still can't get this to work.

Is there any good documentation out there for item-level permissions
(specifically Edit Access)?

It sounds like you've got it configured appropriately. What permission
level are the other people? If Contribute they should see everything
but only be able to edit  their own items. It may be however that you
have people  with approval authority. Approvers can see everything no
matter how the list  is configured. If they also have edit access then
they will be able to edit anyone's item.