Over a year late but perhaps relevant for anyone else with this question, since the comments and answer given seem to miss the point - which is not about deploying to your own server but rather configuring meteor.com hosting to use a custom domain.
Meteor.com offer a free service that is intended for demos and internal betas - the very early days in the life of a site.
You can use meteor deloy without configuration if you are deploying to a subdomain on meteor.com -
meteor deploy myGreatHope.meteor.com
However you can also host your app on meteor.com using your own domain but to do that you need to be able to set up an alias which is done through CNAME A records
These are setup on a server that would otherwise host your site - So you will need a host - it could be really cheap one, and it could provide email hosting for you, ask them to create the A records (or look up your control panel help files) so that they resolve to origin.meteor.com and then you have your site, deployed to meteor.com accessible through your domain name.