You can’t do it with your WordPress.com blog unless you do it as a subdomain, like your website is http://porgy.org and then the blog could be http://blog.porgy.org. For that, you’d have to get the domain name upgrade.
Easy to do with your WordPress.org blog, though. But you have to ask in their forums for instructions, because we don’t do that around here.
That is only possible if you buy the domain upgrade from the “upgrades” menu in your admin window.
I don’t know about wordpress.org – it should be quite possible since that’s what the wordpress software is for – but I have never used it so can’t give you any advice. Try go to the wordpress.org forums – these forums are only for wordpress.com hosted blogs.