How do I make a button/badge for
my shop to put on other blogs?
First off, you need to make an image for your button. 11m2 designed and made an amazing button for the Lab Rats. If you have a logo that's a great option, otherwise you can simply use one of your product photos. You'll have to decide on a size as well. Our logo is 200 x 200 which fits great in our wide sidebar, but may not work for everyone. 150 or 125 pixels are also good widths. When you're satisfied with your image, upload it to an image hosting site such as imgur, photobucket, or flickr.
Now for the technical side of things. You will have to create some coding so you can display your image and make the code visible for others to take and add to their site. This article has easy to follow information for doing just that. Follow the instructions there adding in your image and shop urls where directed and you'll have your code and badge set up in no time.
Getting others to feature and use your badge may be a tricky process. One possibility is to find other shops and blogs that are a similar style to yours, but not competing and offer some cross promotion. You put up their blog button and they put up yours. Another option is the next time you are doing a giveaway or similar promotion, grant extra entries to followers who are willing to put your badge on their blog. These are the two that come to my mind first. Hope this gets you started!