He comes out just after sunset, the easiest way is to play the sun song and enter the graveyard.
They can both be found in the Forest Temple, which you can only get to by being an adult and having the hookshot. You can get the hookshot by beating dampe the graveyard keeper in a race. Dampe can be found in his tomb under a headstone in the graveyard as adult Link. If you are having trouble with the forest temple, google it! :D
After you jump into Dampe's grave, you have to race dampe! This is triggered once you beat the fire temple
First grave at the very left of the graveyard. The one with flowers at the foot of it. Pull the grave out, jump down, chase Dampe, talk to him after you catch him, he gives you the 'special item'
Perhaps you are referring to "Dampe", the grave-keeper's house. Entry to his house requires obtaining the master sword, then turn into big link. Then Dampe will be dead and his house will be unlocked.
In the future, go to the group of graves on the left side of he graveyard. There should be one with flowers in front of it. Pull it back and jump down the hole. You'll find Dampe the Gravedigger's ghost. Race him and at the end you'll receive the hookshot.
You open one of the graves, don't remember which. jump in, and if you see a ghost (Dampe FYI) talk to him. follow him through the race and you will get it as a reward.
Pull the grave with flowers in front of it
Go to the Kakariko Village graveyard and enter the grave in the far left row that has flowers in front of it. Once inside, you must race Dampe's ghost (this is as an adult, btw).
You never meet Zelda's father in Ocarina of Time.
Dampe's grave is in the Kakariko Graveyard. From the entrance, go up, make a left, and pull the 1st grave to the left to get to Dampe's grave.
After entering the graveyard in kakariko village go left and pull back the farthest left grave go in the hole to find a ghost of dampe.
The Legend of Zelda Ocarina of Time does not have a remake on DS but it does on 3DS.