Hold down your finger on any of the icons on your home screen. After a couple seconds, the apps will begin to shake, allowing you to move them around, organizing them how you'd like. You can even pull them over onto a second Home screen if you'd like.
When your done rearranging, press the Home button to lock them into place.
You can learn a TON more about using your iPhone/iPod touch on Apple's website.
They have a place just for tips and tricks like what you're asking, with video tutorials. http://www.apple.com/iphone/tips/
Hold down any icon until they all start to wiggle. Then drag the icons to move them.
To delete webclips or non-apple apps, hold down any icon until they start to wiggle. Tap the little X in top-left corner of the icon and tap delete, then either rate the app or tap "No Thanks."