Click on the picture that looks like the one below:
After clicking on the picture you will be presented with a Enter Network Password dialog box like the one below.
Enter your username and password in the boxes and click on OK.
User Name:
Password:
You MAY, depending on your browser be prompted again for login as shown below:
If you DO receive this second login screen, change your User name to have the domain name preceding your username as shown in the following example:
Once it has verified your security credentials it will allow you into the email system.
When finished, click on the "Log Off" icon. The location of this icon may vary depending on the browser type you're using
Internet Explorer:

Firefox browser: