How do you delete apps on an iPhone 4?

On iTunes
Go to "Apps" section and you can chose to delete the apps you need.
On iPhone
Hold an app for 2-3 sec and it goes to jiggle mode, then tap on the close (x) button on the left hand corner and it asks you whether you want to delete it or not

Yes, I did that but the app appears to still be running in the background.

How come? is it still opened in the task manager ?

Double press the home button (the round button with a square on it) and a line of apps should come up. you can flick left and right to scroll. Hold down an app for 2-3 seconds and then press the red "no entry" button and it will close it.

Then follow Maziar's instructions in 2nd post
Double press the home button (the round button with a square on it) and a line of apps should come up. you can flick left and right to scroll. Hold down an app for 2-3 seconds and then press the red "no entry" button and it will close it.

Then follow Maziar's instructions in 2nd post