Do you have any apps downloading that you dont see...perhaps in a folder?
If not, try going into the app store to the app you are trying to download. If it says installed next to the app, hit your home button and your app should begin to download.
If not, try to delete the app by holding it down and tapping the 'x' next to it. From there, simply redownload it from the app store and your back in buisness.
Still having trouble...?
Try downloading a similar app or go onto your main computer.
- go into the iTunes Store
- Search the app you are looking for in the search bar
- Download it onto your main computer and sync it to your device.
(You may have to cancel the download on your device first before you sync it to your main computer.)
If you are still having difficulties try this
go into iTunes>more>Downloads
look for waiting dowloads there
Delete the waiting download and redoenload the app from the App Store either on your iPad or your main computer
For Future Reference: Usually if you have one download having difficulties, it messes up your entire system which makes using your device that much harder. I recomend the last option I suggested. It worked for me and this other user by the name of britewhitelight