Alerts appear in the upper-left corner of the site. When you have a new alert, a pink bubble will appear with the number of new alerts you've received. There are separate alerts for contact requests and those for any other stories.
For example, when someone sends you a contact request, you'll see the number 1 above the "Requests" button. Click on the the button to view or take action on new alerts.
You can also click these links at any time for additional actions. For example, click the contact request link to find people you might know.