What are the steps for republishing imagery held in archives?
Before requesting publication rights for images it is best to have an arrangement with a publisher, as most institutions require you to provide details about the publication venue, the type of publication (print or digital or both), the print run and so forth when you are requesting the images. Then you have to make a request to the image holder (provided the copyright is not an issue for your, as you indicated in a comment to another answer) either using a web form or by email (in most cases you should be able to figure out from their website who the contact persons for such requests is. They will inform you about the costs, and then you can decide if you go on with signing an agreement (yes, you have to sign a contract with each institution providing images even in the rare cases when the images are provided for free), and they are expected to provide you with high resolution images after the payment (if they charge a fee, as most such institutions do, at least in my field). You surely can crop and process the images as required for the production of your publication. Keep in mind that in the worst case, the process can take months, so it is best to start it as soon as you reach an agreement with the publisher.