I would like to use a few graphics in the book. Is there a specific form or format that you need the approval from the source to be in?
For instance, the cover. I can find the artist and ask permission to use his/her work, but would a simple email stating that he/she has allowed me to use it suffice?
What if the artist has died many years ago and dozens of art dealers sell the same picture? Do I still need to get permission from someone to use the Art?
As an author or self-publisher, a simple e-mail will do it most of the time. Just be sure you've contacted the correct person and that they, indeed, own the rights to the work.
As a publisher, I required a little more from my authors because I was not contacting the original source myself. I had a contract they could use. In some cases, I needed the contract notarized.
Even if an artist has died and others sell the artwork, it still may be protected. You have to do your research to find out if it's protected (then yes, you need permission) or if it's in public domain (no, you don't need permission).
I've mentioned The Copyright Permission and Libel Handbook: A Step-by-Step Guide for Writers, Editors and Publisher by Lloyd J. Jassin and Steven C Schechter before, but I highly recommend it for anyone (read: everyone) writing non-fiction and quoting other sources. I got mine at my local Barnes and Noble, but it's also available on Amazon.
This is a reasonably priced book and has lots and lots of really good information on the topic, including how to tell what's protected and what's not, getting permissions and releases on artwork (and literary works), how to find artists, and sample contracts in the appendix (including ones for art).
There is another very good book, Kirsch's Handbook Of Publishing Law: For Authors, Publishers, Editors And Agents by Jonathan Kirsch, but it's currently out of print and not available at Amazon. It was also pretty pricey when it was in print. This one I recommend to agents, editors and publishers.