You will need to configure the context (click its name in the tree and open the Context Settings tab) and add at least the following:
- site_url: the full url to the site, like
http://mobile.site.com/
- http_host: the domain: mobile.site.com
- base_url: the part after the domain: /
- site_start: the ID of the resource that is the homepage in the context. This is 21 in your case judging from your screenshot.
When you did that, MODX knows most of what it needs. You could also add error_page with the resource ID for an error page.
You will also need a way to have the server start up the right context when a request comes in. What I typically do is make sure that the second/sub domain (mobile.site.com) is configured to resolve to the same folder on the server as the main domain (site.com), and then I install the ContextRouter plugin in MODX. This plugin will look at the http_host you just configured and should work without additional configuration.
Another option is to have the subdomain resolve to a different folder and to copy the index.php, config.core.php and .htaccess files into that directory. Then you would open the index.php, find "$modx->initialize('web');" in the file and change "web" to the name of your context. Third option could be the Gateway Manager plugin.