Not sure if you already figured this out but log into your admin area. On the left hand side hover over Appearance and then click on Themes. From this area you will find a list of themes that you have already installed.
You can click on the Preview link under the picture of each theme to see a preview of your site's content displayed in that theme. You can then also click around inside of the popup to essentially navigate through your site with the new theme.
If you don't have any themes that you like, you can click on the Install Themes tab up at the top and do a search for themes as well as use the filter options. After searching or selecting filters you can then click Preview under the theme thumbnails to see a preview of the theme with some filler content.
If you like the theme you can then click the Install link to upload the theme to your website. After installing you can choose to Preview | Activate | Return to Theme Installer
Preview will create a popup and show the new theme with your own site's content and allow you to navigate around. Activate will activate the theme and show the new design to visitors of your website. The third link is pretty self explanatory ;)
You can also setup your own webserver on your computer using a program like WAMPSERVER for Windows or MAMP for Mac. If this is beyond your ability you can also create a subdomain for your site through your host's control panel and then install another WordPress installation on the subdomain and use the above method to find a theme close to what you like.
Once you find a theme that is close, if you still wish to make edits you can then activate the theme and visit Appearance->Editor and make edits to the theme there.
It's advised to not make edits this way though unless you know what you are doing as you can easily mess up the display of the theme. If you know how to use FTP you should use that as it is the preferred method for editing files. This way if you make a change and something goes wrong and you can't access the admin area you can just undo the change and upload the file back through FTP and start over.
Ok so a little bit more than just a basic explanation but hope that helps!