In short, I don't think that you can use it as a datasource directly. You can change it's appearance - and there are a lot of articles about how to do that. However, actually using it as a data source is a slightly different thing.
Internally, the Content Query Web Part is built around the SPSiteDataQuery object. You can use this to query in the same way as th CQWP, and this will get you a DataTable. You can then bind this to the controls that you want to. E.g.:
SPSiteDataQuery query = new SPSiteDataQuery();
query.Query = "<Where> ... your query here ... </Where>";
// ... Configure your query - scope, types of list, etc.
query.Webs = "<Webs Scope='SiteCollection' />";
DataTable dt = web.GetSiteData(query);
// now use as you wish. E.g.
SPGridView gv = ...
gv.DataSource = dt;
If you mean how do you use this with web part connections - again, I don't think you can.