I am trying to learn Sharepoint on my own so we can implement a website here at my work. The trouble I'm having even getting going is to create a site it wants it on a server. Is there a way to create a site on my local machine just so I can begin tinkering with some of the design features?
If you have SharePoint Server of SharePoint Foundation installed on your local machine, then of course, you can create SP site (or SharePoint Application) on your local machine. If you don't have any of those elements installed, then no, you cannot create SharePoint site.
SharePoint sites, while they are created inside of IIS, require server software and SQL. Think about it like this: if you don't have Apache server, you cannot create Apache site, right?