Transfering database to upgraded site

I have upgraded my site to the newest version and I am ready to finish the change over however I can not figure out how to change the database over without losing customer and product information. Can someone share how to do this? Do I just copy the "original" database and then update the mod sql's and use that? If so, how can I copy the database? I am pretty handy at this stuff but I want to confirm before I totally destroy my site.
Thanks!!

Upgrading to 1.5 is the much the same as upgrading between different numbered version of 1.3.
The instructions are documented in the /docs/ folder of your site files, as well as in the Tutorials section of this site.

But you shouldn't be doing an upgrade to 1.5beta with your live site at this time. The current 1.5 is a beta release for testing and to help mod developers. It is not for use on live sites.