You should already have it. It is PPP.

I went into
Applications>Ubuntu Software Center>Installed Software where I was able to
confirm the existence of PPP.

I then went to Ubuntu Help Center and entered PPP. The first entry was
Desktop User Guide (ppp/modem interfaces). When I click on this, the title
of this page is Network Settings. I have been searching Network Settings
for hours and cannot find it.

Dial-up on Ubuntu ( or any Linux system for that matter ) has always
been problematic. First hurdle is the make of dial-up modem fitted as
some can be coaxed into working with Linux but some will not work no
matter what you do - all down to the way that manufacturers handed
over control to the OS and only considered Windows in their planning !

So the first thing to determine is the make and model number of your
dial-up modem - since you have Windows and obviously must use it to
get on-line currently then that would be the easiest way for you to
find this. Click on [Start] then Right Click on [Computer] and select
'Manage' from the drop down list. Then go to [Device Manager] and look
at the 'Modem' section to see what it says about the one in your PC
then report back.

The modem is an Intel (R) 537EP V9x DF PCI Modem.