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You will need to at least tell us what version of XOOPS you are running. In general-the inbox link in the user menu will be highlighted with a number next to it indicating you have a private message/notification and how many. You can also select the way you wish to receive notifications in your user account-Edit Account. In there you can choose how you would like to receive notifications: Private Messages or Email.
If you are using XOOPS 2.2.x then I believe that PM is actually a module. Then-you will have to install the module if you haven't already. Next you will need to make sure permissions are set for the groups by going to administration/system/groups and checking each group to make sure they have a permission to ACCESS MODULE by putting a check mark by PM Module and then submiting. Do that for each group you wish to allow to receive and send Private Messages.
Hope this helps a little.
Quest