Turn on JavaScript Code Assist Feature
When you install additional AJAX library support the Code Assist for that library isn't turned on by default.
To turn on the Code Assist feature after you install additional AJAX Libraries:
Preferences > Aptana > Editors > JavaScript > Code Assist > Check jQuery
Switch to the Aptana Perspective
If you just installed the Aptana plugin and are trying to get this to work you'll have to make sure you're using the Aptana Perspective to utilize the AJAX library Code Assist feature:
Window > Open Perspective > Other... > Aptana
Using Eclipse PDT with Aptana Plugin
I installed the Aptana plugin to Eclipse PDT and the jQuery Code Assist worked fine once I realized that I was still using the PDT PHP Perspective instead of the Aptana Perspective.
When I switched to the Aptana Perspective it started working.
Install Aptana Plugin before PDT
Sirokov pointed out that he was unable to get the Code Assist to work with PDT and Aptana Plugin unless he installed the Aptana Plugin first and then installed PDT second.