You have a couple different options to accomplish this. First option is to (if your hosting account allows) set up a subdomain and install concrete5 there. Second would require that you install a development web server on your desktop/laptop and develop the site offline. For this you should research an application called WAMP if you are on a Windows machine.

Hope this info points you in the right direction.

The sub-domain is a good idea, but i personally would just create a sub-direcotory (like /c5) off the webroot and install c5 there. Access your development website at:
http://www.yoursite.com/c5
When development is complete just copy everything in that sub-folder (/c5) to the webroot (/), modify your /config/site.php and your done.

I also think this is the best approach, but it is a bit tricky to do this copying because you'll want to clean up that top-level directory before you move the stuff from your /c5/ (or whatever) subdirectory up there -- so create another sub-directory and move everything into that (except the /c5/ directory of course).

And in addition to modifying your config/site.php file after the move, you'll also want to edit your .htaccess file (if you have one) and change the "RewriteBase /c5/" line to "RewriteBase /". Also also as soon as you've done the move you will want to log into the dashbaord and clear the cache (Dashboard -> Sitewide Settings, click the "Clear Cache" button), and then re-run the indexing job (Dashboard -> System Maintenance, click the "Run Checked" button).

After sleeping on it I remembered about the .htaccess file and Jordenlev is correct. If you are using "pretty URL's" you will have to diable the /.htaccess in your webroot and create or copy a new /dev/.htaccess with the changes Jordanlev refered to. I would also NOT move, but copy the files recursively to the /dev directory (just in case something goes wrong). Also do a full site backup for double redundancy. You have an exact copy of c5 in both webroot and /dev and can easily swich back in just in case. Clearing the C% cache may be required and not a bad idea to do anyway.

Thanks for all of the input. I will be taking the subdirectory approach and will let you know how it works. I'm starting to wrap my head around using a cms/website software not loaded on my computer (unlike all others I have used).