You can get an url for a person to sign with by using the service point /envelopes/{envelopeId}/views/recipient
See the recipe.
However, you don't want to send this link in an email since the url is only good for a couple of minutes. Instead, the link sent in the email should go back to your app. Your app would then obtain the signing link and give it to the signer.
Note that by using this api call, your app is responsible for authenticating the signer.
This is a big deal. How does your app know that the signer is who she says she is? Logins? Exclusive control over the username/pw?
Branding
If what you want to do is change the look of the emails that DocuSign sends out, you can do that through the DocuSign "Branding" feature. You can change a gazillion different aspects of how the DocuSign service looks and feels to the end signers. See the Branding manual.
You can affect an account's branding through an API call or via the web app.