i don't think there is really a form per se, but it should tell them about your site and where you will place their link. I also think if the email is unsolicite try to use a non spam subject. maybe like "Willing to trade links?" ---I would delete an email titled "link trade"
If you outline how your link will benefit their site I'm sure you'll get good results. People are selfish by nature. They aren't interested in doing you a favor, but sure as hell want to know what you can do for them. So for example say you'll drive their traffic up, raise their PR, get their rankings up, will expand their brand reach, ect. Don't lie - only say these things if you can deliever.
It's best if you can get a contact name from the prospective company -- it may help, of course, but it might not -- you have to write like a human, not an automated newsletter.
I don't think Eniva (eniva.com) would exchange links. I just want to exchange links with other blogs related to nutrition, vitamins, fitness, supplements, etc.
Just write as a personal email, because most of the websites are owned by individual people, not by company, and then tell them about your website, including content, PR, alexa rank, position where link will be placed, etc.
Short emails just mentioning where you have put other site's link and where you want you link to appear tend to produce best results.