@whatgirlslike - a lot of what goes into a giveaway is up to the blogger and the sponsor - that's why it's kind of difficult to do a tutorial! :) Usually a giveaway works by offering a prize to your blog readers in return for them either following your blog, liking you on Facebook, following you on Twitter, or even just commenting on the blog post. They can also do all of those things for the shop that sponsored the giveaway. You can allow multiple entries from each person or just one.
The sponsor can mail the item to the winner or they can mail it to the blogger who can then turn around and mail it to the winner, that's up to you and the sponsor.
As far as what the blogger does for the sponsor, that's up to you too. Some bloggers will offer a shop feature for the sponsor, while others will offer advertising on their blog for a certain amount of time.
I would say that the blogger or the sponsor would pay the shipping on the prize. Again, this is up to you, but I wouldn't want to have to pay for shipping on something I'd won! :)
As far as where to promote giveaways, I'll go find a great link that aquariann put on the Etsy Blog Team. There is a huge list of places to submit your giveaway. Then you should also tweet it, post it on facebook, and on all of your Etsy teams. It's also a good idea to offer another entry into the giveaway for having entrants post the giveaway to their Twitter and FB accounts.
I think that about covers it! :D