When you are on the site in Safari, touch the icon to the left of the URL bar (it's a box with an arrow coming out of it), although you can choose bookmark I normally choose add bookmark to home screen, this then places the bookmark as an icon on your home screen, I then drag them into specific book mark folders I have made.
To delete icons, you delete the actual apps that go with them (although they can be re- downloaded again for free at any time). Touch and hold an app, they will all start to wiggle, touch the x in the top corner of the icons/apps you want to delete and poof! They will be gone. Once you have finished deleting, press the home button to get everything back to normal.