This document assumes you have set up Growl and it's running and that you have set up at least one account in Adium.
If not, you can download Growl from here and download Adium from here.
The first time Growl and Adium are both running at the same time, you will probably see a Growl notification telling you that Adium has registered itself.
This means that Growl has recognized Adium and can start sending out notifications.
In the Applications tab of the Growl preferences (see Apple menu > System preferences > Growl) you will see there's a line with Adium and in the second box, you can see all different possible notifications Adium has the capability of sending. Eventually you may choose different display styles for different kind of notifications, but this is advanced tweaking.
To get your first notification in Adium, you will need to open the Adium preferences and go to the Events tab.
For each event, if desired you can set a notification.
Select the event, click on the plus sign to add a notification and choose "Show Growl notification".
The amount of possibilities that Adium offers is very large, so take your time testing different options.
These are the different events that you can set a growl notification for:
The Adium trac page has some more information.