1. Add the webpart to your Webpart Page

2. Modify its properties
Enter Mail server address and Mailbox details.
Mail server: http://<mail server address>
Mailbox: <username>

For dynamic webpart type in ? in mailbox field

The My Inbox webpart display your emails as shown.

There is one more way to show your emails through Content Editor WebPart (CEWP).
1. Add a Content Editor webpart to your webpart page
2. Enter the following code to display outlook emails to your sharepoint page.
<OBJECT classid="CLSID:0006F063-0000-0000-C000-000000000046" width="100%" height="300px">
<param name="Folder" value="Inbox">
</OBJECT>
Problems with this (CEWP) Approach
1. It requires Outlook to be installed in your local machine
2. It authenticates with the Logged in user of the Operating System not with the portal.