It says on settlements that have a smiley face it will allow you to share resources with other places? How does this work because I have gathered tons of wood at one place only to find out that my main shelter(red rocket) has no wood at it?

You have to set up a supply line. Once you have rank one of local leader you can go into build mode and highlight a jobless settler you would like to make your supply runner. At the bottom of the screen, once the settler is highlighted, there is a option to set up supply line. Hit the coresponding button and chose which settlement to link up.

Make sure you read the post by JacoZilla on here about supply line tips when assigning settlers to them.