Setting up site as test site not in a domain?

I have my WP site installed on my home PC and used XAMPP to sort that out. I found it very difficult and ran into problems with XAMPP probably, becuase of previous attempts at installing and old passwords. I don’t quite understand how all the various pasword bits fit together: I have one for XAMP, one for MySQL, one for PHPmyAdmin and then another for WordPress….

Anyway, I am ready to upload my first site but I don’t want it as a domain. For now I just want to install it to my own site as a test and possibly, install a second test site as well in the near future. Can I check what I do if I want to install but not as a domain?
I think that I need to make a folder say, test01 and install to that so I will have pulic_html>test01>wordpress and put all my wordpress files and folders in the wordpress folder on my host – is that it? Then do I have to do the install thing on my host or was it enought to do it on my local PC?
My Host provides one database. Can you give me an idea of how I link wordpress to that database. I have also read in the set-up process that WP can have more than one blog using a single database. That’s what makes me think that I could then have another site in test02?
Any advice or pointers would be appreciated.
Thank you