This is standard Send an Email screenshot:
There are 2 options to send email using other email address:
1. My Email Settings
This is option is more for personal usage or need to do by each users if need to do by a team.
- Navigate to Your Name | My Settings | Email | My Email Settings
- Change "What email address would you like to use as your return address?" to the new email address.
Salesforce will send an email for verification to that email address and you need to click the link in that email.
Once verification done, you will notice there are option for you to select a sender email address when compose email from Salesforce, so when recipient reply the email, it will sent to which email address you select.
2. Organization-Wide Email Addresses
This option is for setting additional email address for whole Salesforce users or by Profiles.
- Navigate to Setup | Email Administration | Organization-Wide Addresses
- Add Display Name, Email Address, select either visible for all users (All Profiles) or certain Profiles only.
Same with My Email Settings (point 1 above), Salesforce will send email for verification before it will be available to users.
Once verified, notice additional email available in From when you Send Email from Salesforce.