Whenever possible, I like to copy the actual object rather than making a screenshot. With Excel, I find it better to select the chart and copy (either with Ctrl-C or the Edit-->Copy menu). From there, I can paste the chart into Word, PowerPoint. In this case, you need to paste it into Paint as you were doing with the screen capture. This way you get only the chart.
Once you have an image of the chart that you like, you can get it into your blog. (Most blogging software does not allow for direct insertion of graphics or other non-text from the clipboard.) So, how to get that file somewhere your blog can see it? This answer somewhat depends on the blogging software you use.
Generically, you need to have the image file in a publicly accessible location, such as in your "images" directory on your blog or on a public photo-hosting like Flickr. Then you have to create the link to the image, which most blogging tools can help do. Many blogging services also have the ability to create a thumbnail (small version to save bandwidth) with the full-sized version viewable by clicking on the picture.
I see that Blogger and TypePad have it as part of the entry editing screen. Movable Type has a separate File Upload area which then lets you create a post with the file iTypePad. Wordpress has a function that allows you to upload files in the posting screen.