In your FTP Client (File Zilla is a good one) just move all the folders you have in htdocs in a new folder called blog. Beware that if you perform such change all the links you you manually created will not work anymore! So if you starting now go ahead, otherwise think about it.
It's not easy as or straightforward as just moving the files because the link into the database that holds your posts will break, but it can be done. See this entry on the Wordpress site:
I agree with Stuart ... the best way to move your content is to create a fresh WordPress install and then export your original content to be re-imported into the new blog.
Yes I agree with Stuart too. Is there any plugin doing the wordpress migration from root directory to another.
Do you guys think..Oh sorry charly too gal..is there any demand for this type of plugin.
By the way wordpress 2.5 just out, looks very promising.
If you start over "fresh" or move the blog in any way, be sure to do 301 redirects on all of your current posts and pages to the new location so that you don't lose any link love you've already built. If you have any traffic coming from the search engines currently, then this is mandatory. It will be as if you no longer exist. There is a plugin that will help you with this, http://urbangiraffe.com/plugins/redirection/.
I think the bigger question is why are you moving it?