Not only can you move around the existing icons on your home screen, you can also add new ones. To move around current icons, simply touch an icon for few seconds and they all start to shake (so cute!). While shaking, just toss 'em around where you want them to be. Hit the home button to set.
To make a new icon, open Safari and find the site you want to be one click away from. When on that site, zoom into the page (what you zoom in on will be the icon on your home screen), press the plus sign at the bottom of the screen, and select "Add to Home Screen." You'll be able to edit the title of the icon and then touch "Add." And Voila! Your new icon pops up on your customized home screen.