I Need To Change My E-mail Address For My Steam Account

1. Right-click on the Steam icon in the System Tray and select Settings or press the Settings button in the Steam menu. ('Preferences' for the Mac client).
2. Press the Change contact email button.
3. Enter your Steam Account password along with your new email and click Next.
4. Check your new email and click the link sent to you by Steam Support. Do not close the Steam dialogue box while you retrieve the email. If you didn't receive this email message, please Contact Steam Support or try using a different email address.
5. Return to Steam after you see the Success! page. The diolgue box in Steam should now confirm the email change. Please click Finish to complete the process.
6. View your Settings in Steam and make sure the email is updated.  

If you see an error message anytime during this process please Contact Steam Support with the error or try again later.

https://support.steampowered.com/kb_article.php?ref=3176-RTKC-3810