Joomla - Create another page

it depends on where you want the page to go. - is it another menu item?  or will it be linked to from a page?  or is it going to be a blog or news style page?  (many articles on one page)
it is usually done by creating and Article with content, but it may depend on what category you placed the article in.
so I would check  is it "published" and what category and what level of user can see it  
what version of Joomla is it.
can we have a link?

Creating a new page in Joomla involves 2 steps...
1) Creating a new article with content (new page)
2) Create a new menu item in the top or side menu and LINK THE ARTICLE to the menu.

when you create the new menu item... select type as SINGLE ARTICLE and then link the newly created article to it.

if the page link is a direct link menu.... thew url will be www.mysite.com/newpage.html 

if the new menu is a submenu then the new link will be www.mysite.com/menucategory/newpage.html

let me know if you understood ... if not then I will paste screenshots of the process.

thanks,
Prasadh

"I tried leaving it uncategorized and it is using the pages header and footer which I don't want.  I just want the page's content itself."

This part of your question involves the TEMPLATE Construction part... means whatever new page you do as per above instructions will be shown in the COMPONENT part of the template... and if the template has a Header + Footer... it will also be shown in the new page.

if you dont want the header + footer... you will have to create a new template for it or modify the existing template using if /elseif statements....  it is complicated and you will be able to do only these changes ONLY if you know how to create/modify  a joomla template yourself.

if not, you will have to be content with the new page with header + footer OR take help of a professional developer/designer for that part.

thanks,
Prasadh