There are a few ways of going about getting a banner for your blog. Any hyperlinked image (photo, banner, logo etc) will work.
Buy one: There are a lot of web designers that will make a 125 x 125 px banner for a very reasonable price so it's something to keep in mind. If you have a blog template that you love, you can usually ask the theme creator to help you with making a complimenting banner.
Make one: do you have any photo or graphic software? If not... you can always play around with an online banner maker. Here's one (haven't tried it just found via Google): http://banner.fotor.com/
. PikMonkey is another I've heard of.
Many new bloggers start out with a cropped photo of some sort. My biggest piece of advice if doing this is for it to be a clear image. I see a lot of pixely, blurry and skewed banners that people put out and I can't imagine anyone would grab it. Remember that if you are asking for people to put it on their website/blog- you wont' get a lot of takers if it's an eye sore!
Size: I suggest a 125 x 125 px banner or smaller. Sidebars are precious real estate so over-sized banners can either deter people from grabbing it or break sidebars. 125 x 125 px is a universal button size.
When you have your image ready, you'll want to use a text area form box to offer an html code to your visitors.It will looks something like this:
<textarea rows="4" cols="25" name="Banner Grab"><a href= "http://www.myblog.com"><img src="http://www.myblog.com/images/banner.jpg" /></a></textarea>
You should put the banner image above the text box, so people know what the banner will look like. The banner & form box would be something like this:
<div align="center"><a href="http:/www.myblog.com"><img src="http:/www.myblog.com/images/banner.jpg" /><br>
<textarea rows="4" cols="25" name="Banner Grab"><a href= "http://www.myblog.com"><img src="http://www.myblog.com/images/banner.jpg" /></a></textarea></a></div>
The above code it the banner & textarea box wrapped in a centered div. You can change the rows & cols (width/height) to fit your sidebar. And make sure to replace http://www.myblog.com
with your blogs URL and replace http://www.myblog.com/images/banner.jpg
with the link to your banner. You have to offer a hosted banner... not one from your computer desktop.
As for adding this to your website depends on what kind of platform you use.