How to expose a RESTful Web Service using Meteor
I did a full write-on on this in Meteorpedia:
http://www.meteorpedia.com/read/REST_API
The post reviews all 6 options for creating REST interfaces, from highest level (e.g. smart packages that handle everything for you) to lowest level (e.g. writing your own connectHandler).
Additionally the post covers when using a REST interface is the right or wrong thing to do in Meteor, references Meteor REST testing tools, and explains common pitfalls like CORS security issues.
I originally answered this question here, but to recap:
For adding RESTful methods on top of your data, look into the Collection API written for Meteor:
https://github.com/crazytoad/meteor-collectionapi
As for authentication for accessing the database, take a look at this project:
https://github.com/meteor/meteor/wiki/Getting-started-with-Auth
Both are definitely infantile in development, but you can create a RESTful API and integrate it with a mobile native client pretty easily.