EDD: If they're synth based effects as apposed to manipulated samples etc or found sounds, you might be better off creating your own FX using a plugin, however I can't see the video you've posted so I'm just guessing.
Many websites have sound effects sorted by categories, you can probably search by the any key word (e.g., whoosh). Many have free samples available (with lower bitrate and mono) and charge you some $ for high-quality stereo ones.
Google is your good friend :)
[Gilles Marchand]"I'm totally new at this just getting into after effects cs4 this past weekend.."
I didn't attempt an AE project for a couple of months after I first opened up the software: too many basics to learn before I could even know what I could do, to say nothing of how to do it.
Are you over your head yet? If you have a tight deadline, I wouldn't count on making that open in AE, because AE is NOT the kind of software where you can say, "I want to do just this one thing, and it looks like this example -- what are the steps?"
You can follow the steps to make a table from a text file in Microsoft Word, but AE's just a little different.
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