There is a simple two-step process to adding new email senders when using Soapbox Mailer. One update needs to be made in Amazon Simple Email Services (SES) and another needs to be made in Soapbox Mailer.
In Amazon SES
1) Login to your Amazon Web Services Console account at https://console.aws.amazon.com
2) After successfully logging in, click on the link to Amazon SES: https://console.aws.amazon.com/ses/home
3) On the left side of the screen, under the Navigation heading, click on the "Verified Senders" link: https://console.aws.amazon.com/ses/home?#verified-senders:email
4) Under the Email Addresses tab, click the Verify a New Email Address button
5) In the popup window, enter the email address for the new sender which you wish to use, and then click the Verify This Email Address button
6) Check the inbox of the email that you entered in #5 for an email from Amazon, and then click the link in that email
7) You can confirm the status of your email's verification at any time by going to the Verified Senders link: https://console.aws.amazon.com/ses/home?#verified-senders:email
8) Make sure your new verified sender has the bounce and complaint notification topics assigned (otherwise Salesforce won't get back bounce and complaint responses)
Note: If you have many sender email addresses or if your sender email addresses change fairly often, you might consider verifying your domain instead. This involves a little more setup upfront but once completed, any email user with your domain will automatically be verified to send emails. You can find more information about domain verification here.
In Soapbox Mailer
1) Go to the Soapbox Mailer app in Salesforce
2) Click on the Senders tab
3) On the Senders Home page, in the Recent Senders pane, click the New button
4) On the New Sender page, enter the email address and name of the new sender (NOTE: do not include any punctuation for the Sender Name field, only alphanumeric characters)