You should be getting 2 emails.
One email is what I call the notification email. That one goes to the To: address in the CF7 form that you made (usually that is set to your wordpress admin email address, unless you changed it). That one is just to tell you that a visitor came to the site, filled in the form, and was sent an email (or given a link on the page or whatever).
The other email is the one that goes to the email address that the website visitor typed into the form that was displayed to them on your page. This could be any email address. If things are working correctly, then it will send an email to that address and that email will have a link to the download or an attachment (or both). It is a common problem for this email to not arrive because it gets blocked by the email provider (like Yahoo Mail for example).
So, for you to test your setup, you need to make sure you are getting both emails. Thus, when you go to your page as if you were some random person on the internet, make sure you put in a test email address —- NOT the same one you are using as your wordpress admin email address. Then, submit, and see if you get an email to that address and another email to your wordpress admin email address (or whatever you set it to when you made the CF7 form).
Update this w/results of your test etc