Touch the app and hold your finger down until all the apps start to jiggle. You will see a circled "x" in the upper left corner. Tap it to delete an app. When done press the Home button.
You cannot delete any pre-installed iOS app.
If there is No 'X' on any apps you have Downloaded... then check in Restrictions... Settings > General > Restrictions > Deleting Apps = Off / On
If the app is in iTunes, then you delete the app in iTunes (Select the App and Press Delete on your Keyboard). If you then sync with your iDevice, the app will also be deleted from your iDevice.