In the vSphere Client click on Administration, then vCenter Server Settings.
A new window will appear. Select Mail on the left hand side, then specify the address of the SMTP server you would like to send out email from, as well as the email address you would like to use to send alerts from.
Once completed, click on OK button. Next, highlight your vCenter server in the top left, then click on the Alarms tab on the right, and select Definitions.
Select the Alarm you want to send email alerts for and right click on it. Then select Edit Settings.
In the Alarm Settings window, click on the Actions tab, then click on the Add button.
Specify the Action, email address you want to send the alert to in the Configuration box, and select the criteria for the action on the right hand side. Once done, click on OK button.