The person who is delegating the sending of Email will do:

1. In Outlook, go to Tools, Options, and click on the Delegate tab.
2. Click Add to go to the Global Address Book and select the name of the individual you are
    granting access. Click OK. You do not have to select any persmissions for individual folders.
3. At the bottom of this window, click the option that says Automatically send a message to
    delegate summarizing these permissions.  This will send an email to the person informing
    them of their new capabilities.

The person is who going to send the email on your behalf, would do the following:

1. Click New to create a new email message.
2. Click on View located on the main toolbar, and select the From Field button. This will 
    insert the From field onto the email message format.
3. Click on From and select the person you are sending the message on behalf.

The rest is just like sending an email. The person receiving the email will see that one person sent the email on behalf of the other person.