How to create a separate web page menu to be used only on one of my web pages?
Add a new menu to the site.

Go to Structure > Menus > Add Menu

Once you have added a menu, and the links, this menu will now be available as a block.

Go to Structure > Blocks and assign the new menu to a region.

under that block settings, you can define which URL you would like the block to display on. Set that to the URL of your page, and you're good to go.