For iPhone
It's easy to add a bookmark to the home screen on your iPhone.
When viewing a web page, hit "+" and select "Add to Home Screen".
For Android Phone
On Android it's slightly more involved:
Step One - Bookmark the website page you want to add to your phones home screen.
Step Two - Go to the home screen you want to add the link to and with you finger "long-press" in an empty space to bring up the "Add to Home Screen" menu
Then:
Select "Shortcuts"
Select "Bookmark"
Choose your bookmark!
Smart Phone Home Screen Help