Growing it is no different than growing any other tomato. However, unlike regular tomatoes, harvest time is not as obvious since there is no real color change. But it is still easy to tell when they are ready. As mentioned earlier, when the full sized fruits begin to show just a little light yellow color somewhere(usually on the shoulder or the bottom of the fruit), they are ready to pick, and at this point will have a a good balance of sugars and acids and a flavour you will most likely enjoy. Anyone who likes red tomatoes will probably like Granny Smith as well. This will probably be the best green tomato you have ever tasted!
Granny Smith tomato would be excellent for making salse verde - a great substitute for those golf ball sized tomatillos. It's also great for fried green tomatoes - the big slices are nice and firm and hold together very well when frying or grilling. Also try full slices on a burger or sandwich for a great new taste experience or cut them up in wedges for salads.
Here's some confirmation from Ed Eckhoff, a farmers market grower and vendor in Woodland, California, who trialed Granny Smith when it first became available. He agrees the big slices are great for grilling and frying. Another vendor there grills them, people try them, then go to Ed to buy fresh Granny Smith tomatoes to take home. They taste better than other green tomatoes, which are often bitter, and they are very firm, so they hold together on the grill.