Here is it how it works normally on default WP setup:
When any user (including you) hits the submit button on the contact form:
* An email is sent to the “Email Address To” address given in the plugin settings
* The email that is sent will use the sender’s email address as the “reply-to” address
So when the recipient receives the email, they can click reply and the email will be addressed to the “reply-to” address.
If that is not happening in your case, there could be something (like some other plugin or theme) that is interfering with normal functionality.