I have a site - "http://trainingbjj.com" I want to be sure that URL above and "http://www.trainingbjj.com" are seen by google as the same site. I think it is, but how can I be sure?
You must create an account in Google Webmaster Tools and add your site there. Then go to Site configuration -> Settings -> Preferred domain and set it to the url that you want.
another way is to use mod_rewrite (if you use apache server) in a .htaccess file. If you create a rule all non www requests will point to www. also there is a meta tag called "canonical" where you can tell google which one (www or non www) . however, I should warn you, Google probably is not penalizing you or spliting link juice between the two, many highly ranking sites use non www and www with no problem what so ever. Cheers!
Choosing your preferred domain is the best way and I suggest go with how Google ranks your site. If Google sees your site with www, then choose your preferred site URL in Google Webmaster tools as www.