OK, the basics are...
Whatever they are sending the mail from will have the details of two servers setup, the relevant one here is the SMTP server (otherwise known as the outgoing server)
the SMTP server can be setup in two different ways....
1) you use the SMTP server that belongs to whoever your ISP is (so who you pay for your connection), this will work without a username and password but will only work when you are connected to your own internet connection.
2) you use the SMTP server of your email provider (if it's different to the one above), to use this you need to enter a username and password to authenticate with the server but once the username and password have been entered you can use the server to send mail from anywhere in the world, regardless of whos connection you are using.
So what is required is....
Who supples the email (talk talk)
Who supplies the connection (is it talk talk too?)
And, most important, what mail software they are using.
With the information above myself (or others) can easily give brief instructions on what they need to do to get it working.