If for some reason, you do not wish to use the delete_account.htmlt template, you may create your own web page, allowing members to delete their account, and upload it to the Member's Only Area through the Setup->Manage Web Site menu of the Admin Control Panel, by completing the following:
First, your HTML form needs to <FORM> tag, which is:
<form action="members_only.cgi?~authtext~&action=delete_account" method="POST">
The only other requirement is one text field, which the member must type "CONFIRM" into, to confirm their account deletion. This text field must be:
<input type="text" name="confirm">
If you would rather not require members to confirm their account deletion, and instead, only need to click on a submit button, you can use a hidden form field instead, such as:
<input type="hidden" name="confirm" value="CONFIRM">
Last, you simply need to add a submit button to the form, such as:
<input type="submit" value="Delete Account">