Outlook.com's equivalent offering,
https://domains.live.com, is free (Hotmail also offered it, but they've changed the branding). I've been running my email on there for the better part of a decade. To those who point at Office 365, that's similar but different, and it costs money.
If you want a guide, this one seems pretty good:
http://www.omegaweb.com/2012/09/how-to-configure-a-custom-do...
Between the mistaken despair over having no good free alternatives to Google Apps and the platitudes and awe over the Gmail/Google Drive integration (which Hotmail/Skydrive have had the exact equivalent of for years) a couple weeks back, I'm starting to wonder why nobody here, when they are all quite tech-literate, seems to have any clue about Microsoft's honestly rather impressive cloud offering.
Most likely they're all in denial.