When You Can Find It
Before you can begin looking for the hookshot, you must have at least completed the events in the Temple of Time. After finding the central room of the Temple of Time, Link will be sealed there for seven years. It is only after awakening as an adult that you will be able to find the hookshot.
Location
Go to the graveyard near Kakariko Village on the eastern side of Hyrule Field. Locate the grave decorated with flowers on the left side of the grave yard. Approach the gravestone, hold the "R" button and pull the analog stick back to pull the grave open. Drop into the exposed hole.
Getting the Hookshot
Talk to the ghost of Dampe the gravedigger in the cave under the uncovered grave. Dampe will challenge you to a race, then fly off suddenly. Follow the floating flames he trails behind while avoiding enemies. If Dampe gets too far ahead and you lose him, you can return to the cave's entrance and speak to him again to restart the race. When you catch Dampe at a dead end, he will reward you with the hookshot.
How To Use the Hookshot
Press the "Start" button to open the menu and move the cursor over the hookshot. Press one of the "C" buttons to assign the hookshot to that button. Leave the menu screen. Press and hold the "C" button you assigned the hookshot to. When you release the button the hookshot will fire. You can use the hookshot to stun enemies or retrieve distant items. Most importantly, you can use the hookshot to grapple onto certain surfaces and pull yourself across gaps.