Prepop the email into an email submit. Once they submit their email, send them on over to a second email submit. Keep prepopping on every submit.
Or, you could just prepop 2 to 4 email submits into different tabs/windows after they sign up.
If your newsletter double optin, you could use the thank you page to tell them how to active their subscription to your newsletter.
If your newsletter is single optin, tell them what to expect from your emails -when they will receive 'em, what the content will be, and how they can use them. Warm up the traffic!
Maybe ask them for additional information (age, sex, location, etc.) which you could use to prepop offers in your emails to them.
Or, you could just follow DKPMO's advice - show a related offer.