i would guide you through this in a tutorial.
1) Create a new project in xcode using view application template
2) Open up your view's xib file
3) Drag a UITableView and a UIButton from the library to the view.
4) Select your UITableView view and checked the hidden property.
5) Go to your view's header file and declare two IBOutlets (for your button and table), 1 IBAction (for your button's target action).
6) Link up the outlets to the respective UI objects in your Interface Builder and set the target action of the button (touch up event) to your controller.
7) In your IBAction, set the hidden property of the UITableView to NO and button's hidden property to YES.
8) Volia, you should see your table view now when you click on the button and the button would become hidden after you clicked
I skip the part on adding the tableview delegates so you will not see anything in your table. You can check them out on Apple's UITableView example.
EDIT:
In your IBAction for the button, put something similar like this
- Require a navigation controller:
[self.navigationController pushViewController:putTheNameOfYourTableViewControllerHere animated:YES];
- Present in a modal view:
[self presentModalViewController:putTheNameOfYourTableViewControllerHere animated:YES];