There are a couple of ways that you can do this. One way is to use OAuth2, which requires that your app be able to handle a callback from VersionOne. The second way is with a new and much simpler approach that was just released yesterday, and that is VersionOne Access Tokens. Access Tokens do not require that you handle a callback, you simply login into VersionOne, create your token, then use that token in the HTTP requests that you make to the API.
Note that Access Tokens are only available in the Winter 2015 release
Hope that that helps...
VersionOne Product Manager