I have sponsored many blogs to promote my various sites, and the arrangements are always so different depending on the blog and what is needed. I have sometimes sponsored blogs because the blog owner was in financial distress, so it was like a favor where I gave them a payment in exchange for a link and other promotion over the span of a pre-determined period of time.
Other times I have given away free products to blog owners so that they can run contests with my products as well as drive traffic to me.
I have also paid for bloggers to write posts that are about one of my sites or products, so it was like a one time thing, and other times it was a long term thing where the wrote an update every few weeks about a project I was working on and placed a link to me on their blogroll.
I think the most important thing is that you are flexible, and unless you are dealing with someone who already sponsors blogs, you have to be prepared to explain the advantages of sponsoring you as many people will fail to see the promotional potential if they are not familiar with the concept of blog sponsorship.
The blogs I sponsor often tell me that it is hard to find sponsors - that may be just with the niches that their blog is in, but I think that once you get a sponsor, you should likely have a long term relationship, because all the blogs I have sponsored, I always renew my arrangement, unless the cost was too high and I did not see the value in what I got in return.
Rates for blog sponsorships for me are based on verifiable traffic, high Google rankings, a match to whatever I am promoting. Sometimes I offer bonuses, like if I am trying to promote a product, I may a set fee per month and if I get more than X number of signups from the site, or X number of sales, I pay more - it all depends.
Feel free to send me details of what you are looking to sponsor and if me or someone I know is interested, I can let you know ...