Instructions for mapping a network drive on Windows XP can be found here
Instructions for Windows 7 can be found here
To map a drive to the web server, in the folder box type \\utpaweb\sharename$ using your share name. Make sure to add the dollar sign at the end. If this does not work try \\18.104.22.168\sharename$. Make sure the box that says Reconnect at Logon is checked so that the mapped drive will be available to you even if you logout or reboot your computer.
If you are logged into the machine with your domain account (which is your UTPA username password) then you will not be asked for a username and password. But if you are not logged in with your domain account then you will be prompted to enter your credentials. In the username box type utpa\ and your password to connect.