I recommend looking for a small publisher if you are looking to start out as an editorial assistant. Even doing this work for the smallest of companies is still experience, and it can lead you on to bigger and better things.
Many online publishers still need editorial assistants to help with a lot of the organization and editing that goes on at their main office. Usually online publications deal with greater volumes of materials, so there is more opportunity to get some hands on experience with the books coming in.
A great thing about online publications is that you can often telecommute to work. Giving you experience, while still being able to hold down another job if need be.