I am not sure exactly what you are trying to do.
If you want to use your HTML form, without modification, then you will have to do some programming to make the script that manages the form submission send the information on the form to Constant Contact (and then perhaps send the data someplace else?). In the forums on this site there are several variations of form submissions in different scripting languages. There is also a sample PHP based script (and corresponding HTML form) here.
Alternatively, you can use the 'Site Visitor Signup Form' HTML creation wizard from within your Constant Contact account to define a custom form for your account. This approach requires no 'scripting' and it creates a form which submits directly to your account.
Tom M Group Product Manager – Content Editing Constant Contact