Installing Joomla can be pretty intimidating if you've never done it before, and if you don't have experience with your web host's control panel, setting up a database, unzipping files, etc.

How you install Joomla goes something like this:

1. Get a domain name at a domain name registrar (GoDaddy, 000Domains, etc).
2. Get some web hosting. (MidPhase, BlueHost, eMarkHosting, there are many others)
3. Make the domain name point to the web hosting. Wait for propagation to happen (24-48 hrs usually, though shorter and longer times are common). When you can go to your domain name and get your site, you're ready to go to the next steps.
4. Log into your host's control panel.
5. Create a MySQL database and a database user, and make them talk to each other. (If you have CPanel installed as your control panel, there's a great wizard that walks you through the process.) Make note of your MySQL database username and password.
6. Download Joomla.You want the most recent 1.5 version. There's a link on the left side of the home page.
7. Upload the zipped copy of Joomla you just downloaded into your web hosting space.  Some control panels have a nice file manager that lets you do this pretty easily; otherwise, you'll need to use FTP.
8. Unzip the copy of Joomla.
9. Go to your website on the front end, i.e. www.mysite.com.  This will put you into the rest of the Joomla installation.
10. Follow the wizard. You'll pick your language, enter the database username and password, enter some FTP information, have the option of installing sample data, stuff like that.
11. Delete the installation directory from your website.
12. Now you're ready to configure Joomla.

Yes, I'm vague on a lot of details because so much depends on your individual web host.

But here's the key: once you unzip Joomla in step #8, do not STOP installation until you've completed the full process.  When you unzip Joomla, anyone going to your website will see the installation screens. No login is required to see the installation screens. Anyone can click through the process and get it done. It's true that it's unlikely you'll have the database username and password, so it would be hard to complete the process.  At best, it's just unprofessional to leave a Joomla installation screen hanging out there. At worst, you're leaving a pretty wide open door to Bad Things Happening.