First of all..
Welcome Aboard,
fabadekic! You've got a perfectly reasonable question.
You may be able to find some info in the Finder "Help" menu, the info, of course, is about the OS, not really the Finder.
The solution you are looking for, I believe, is called "Archive and Install." It will actually not remove anything but will preserve your old System files in a new folder while installing the new one. Just be sure you do
not ask for the "Erase and Install" method.
OS installers would not normally do anything to files in your user folders, anyway. The only things they update/reinstall are System files. The Archive and Install may even leave any prefs/plugins/caches/etc. that many apps need and use. If they are not left as is, they will be moved to the "Removed System" folder along with all the old System files, anyway. You can then manually return them to their proper place in your new System.
Another warning, however, if you are experiencing problems in a particular program, you may only need to reinstall that one app (after moving or renaming any pref files it may have).
I would also second the concerns about making a backup of your data/work before doing his Re-Install. External drives are becoming very low priced, just set aside a few dollars every day for a month and you'll have more than enough to buy one. Your internal drive is too fragile to trust all your work since you bought that computer to
not have a continuos back up plan.
Perhaps you could answer a question from "us," however. Why do you want to make the install
without making a backup?
Do you have a regular back up plan?