Using Gmail to send from your own email address
- Sign in to your Google Apps email.
- Click the Gog Symbol in the upper-right and select Settings along the top of any page, and select the Accounts tab.
- Under Send mail as, click Add another email address.
- In the Email address field, enter your name and alternate email address.
- Click Next Step >> and then click Send Verification. Gmail will send a verification message to your other email address to confirm that you own it.
- Locate the message from Gmail. Open it and and either click the link contained in the message or enter the confirmation code in the Accounts section of your Google Apps email settings.
Once you're set up: sending mail
To use one of your alternate sender addresses, click the From link when you compose a new message. If you're replying to or forwarding a message, click the field where your recipients are listed, then click From. After clicking From, you'll see a drop-down menu next to your address, where you can select the email address you'd like to send from.
If you ever need to edit the name, configuration or reply-to address, go back to your settings. Click edit next to the address on your Accounts tab. To delete an address, just click delete.
The above is taken from the Google help article
Also here's the link on how to do iyt using Hotmail Or Outlook as it is known now.