Hi --
No need to apologize, everyone was new once.
Let's see. What version of SharePoint are you using? With WSS 3.0, you can actually have multiple forms associated with a single library -- called 'Content Types'. However, your users would still find those under the 'New' menu in the library.
Are your forms bound to a database? If they aren't, you probably will want your users to fill them out and save the XML that InfoPath generates so that they can see what they filled out again. If they are and you don't want your users to save the XML, you might want to create a document library and publish the templates to the document library as if it were a network folder, instead of as the template for a form library.
You see, when you publish a form, you tell it where its location will be. When you then move the form (like in your description above) to a new folder, the form gets insanely angry and proceeds to make your life difficult. Just teasing! But the form template is aware of where it is supposed to be located, and you can't just drag it about.
Here is a link to an Office Online article about form publishing that might help you understand the concept a bit better. Oh,and here is a great lab, you might want to check it out as well. It is for 2003 but a lot of the same principles apply to 2007.
I hope this helps....