Adding to what Sim' said.
There's a button at the top of most pages- "user cp". Click that, and choose "edit options". Make sure that the followinf options are all set to "yes":
"Enable Private Messaging?" (would be Yes anyway)
"Send you an email when you receive a Private Message?" - I like this because sometimes it helps me to realise there is a message
"Pop up a box when you receive a Private Message?" That works most of the time, but sometimes it does not- that's why the previous option is good.
**Also**, if you have clicked the "Pop up box" option, then go into forums, and click the "back" button, you may get the Pop up box again. If that happens, refresh the page (F5, or click the "refresh" button at the top of your browser).