The contact form and quote form is setup to use Formmail, however you may need to use a different script for this setup. You will need to read the instructions included with the other script you plan to use to see how it is setup. Every script will be a little different and we can only give you an outline of what you will need to do to set this up.
The fields where people enter their name and e-mail and so forth is generally the same for all form scripts. You will probably not need to edit these.
The hidden fields are probably what you will need to change. Open the contact.htm or quote.htm in Notepad and look for the following lines listed below:
If you are using a different script you will probably need to remove all the above lines and replace them with the hidden values from your new contact/mail script. You will need to see the instructions that come with your new script to see how this gets setup.
Some hosting companies may already have a contact/e-mail script already installed for you. However, keep in mind that in most cases setting up the contact script using Formmail or another script will involve a two step process. One step will be adding or editing the hidden values, the other step will be installing the script in your control panel or into your cgi-bin directory in the hosting upload area.