if i decide to build a world wonder that says something like build it faster with stone, does that mean i need access to the stone or does it mean that the city that i build it on has to have to a quarry in the stone mine AND i have to work in order to speed up the wonder buliding process?

thanks

You can build any wonder as long as you have the technology which gives access to it, e.g. literature for the Great Library and metal casting for the Colossus.

If a wonder says it can be built faster with stone look at your cities resource box. If stone is present you will recieve a 100% increase in hammers while building the wonder. This means you need a quarry on the tile with stone and that tile has to be connected in some way to the city building the wonder.

Yea, what Thedrin said. Basically the stone has to show up in your city with the other resources (gold, clams, etc). These are displayed in the city menu on the top right. Open city menus by double clicking the name.