Adding a Flickr Badge to your Blog is very easy. You can have it display your own pictures, or those that other Flickr users have made public.

First you need to create an account at Flickr (this is FREE)
Then you need to go to the "Yours" part of the Flickr site. Part way down on the right side you will find an option to share your photos. Click on the Flickr Badge link.
Decide which type of badge you want then click "Next: Choose Photos"
Now you have to decide what photos you want to share (I chose "everyone's for this display) The choice is yours. When you are finished, click "Next: Layout" or "Next: Colors" based on whether you chose "HTML Badge" or "Flash Badge"
This is when you customize the badge to fit your site (select size and/or colors)
When that is done click "Preview & Get Code"
At this point you still have the option to modify how your badge looks and operates.
Or, if you are happy with how it looks, click in the code box and see that everything highlights, right click on the highlighted text select copy then go to your blog/site template and paste it into the area you want it to appear in, on your site. If you have problems making it appear on your site properly, try one of these forums for help.

Blogger Forum http://www.bloggerforum.com/
Web Logs Forum http://weblogs.about.com/mpboards.htm
Blogger Talk Forums http://www.bloggertalk.com/
Blog Connection http://www.blog-connection.com/blog-forums.htm