1. Make sure that you have been given permissions to send-as the other email account or distribution group.
2. Open a new email, click on Options along the top menu. Select "From", this will add an extra field to your email.
3. Click on the new From button that appeared, type in the address that you want to send from, or select it from the address book and click OK.
4. Send the message

You only need to type in the address the first time, any following times autocomplete will fill that in for you.

You only need to add the extra From field once.