I'll use this answer to try to help/guide @peifa. I'll do so by enhancing my answer in multiple steps (iterations), depending on which parts need more details etc as per peifa's knowledge. To Peifa: please add comments to this answers to confirm, ask extra questions, etc where appropriate, OK? And try to EDIT your question instead of adding comments to it (that is not really helpful, since too time consuming to digest I feel). Like the comment about "local host", put that in the question, and then delete that comment again. To anybody else: feel free to edit my answer to refine, correct, etc.
Assumptions: current live (production) site is D6, ultimate deliverable is to REPLACE it entirely with a D7 equivalent, in production status also.
Approach: clone the D6 version from production environment to some TEST environment, which is what in the original post (OP) seems to be called "subdomain". I'm assuming you're using apache as the webserver (if not: what else)? And since I do not see "localhost" or "virtualbox" or anything similar, I assume anything related to the upgrade is happening somewhere online. If not please enhance the OP to claify.
Step 1: update your a apache configuration, to add the config about the root folder for the D7 site and the subdomain name (as it will be used in the URL to surf to it)..
Step 2: make sure you're aware of the upgrade instructions.
Step 3: Upgrade Drupal core (and the database) from D6 version to D7 version. Need I provide more details on that?
Step 4: Upgrade relevant contrib modules from D6 to D7. Need I provide more details on that?