iPod apps show "waiting" under them. What is going on?

How do I do #1? In iTunes I don't see how to update/download Apps? just music, podcasts, movies, radio and tv shows.

The WiFi is working fine.

No, I haven't synch's the apps to the computer yet.

Here is the background info:
The iPod was plugged into another computer that had some songs in the library and they were synch'd to the new iPod Touch.

I installed iTunes 8.1.1 on a laptop and I wanted to move the song files to this laptop and use this laptop and the main computer.

Therefore, there isn't any apps on this laptop's iTunes library.

I don't know what she downloaded, I just see the icon but I was under the impression that the iPod Touch came with a full screen of apps, 4 rows by 4 columns, out of the package?

Ok, I clicked on the App Store icon on the iPod and I can see that one of the icons is a game called Hanoi by Ian Marsh (Free). Another one looks like it is called Jelly Car (my daughter is 9).

Given that information about the apps, are you suggesting that I can use the iTunes software on the laptop and redownload the apps then synch them over. Ok.

Ok, I redownloaded the Hanoi app using the iTune software and it made it to the App Library on her laptop, then I did a synch by using this path File | Synch to iPod and still the app is unchanged (still says waiting) and the app from the App Library did not get synched to the iPod. I've tried tapping the Hanoi app on the iPod but that does nothing.

Any ideas?

I clicked App Store on the iPod and when I went to those games they show "Installed". When I click on the "Updates" on the bottom right is says "All apps are up to date".

Would is just be easier to just delete them and resynch them? In this case they were free but if they cost me money, I would be a little upset and now I am a little weary that these apps can be money down the drain if they end up like this.