You should let them get used to you first, let them know that your voice means food Talk to them every day, when you turn on the light, when you feed them, when you turn off the light, and in between.
Then gradually start dropping the food with your fingers closer and closer to the surface. Eventually you can start holding pieces of veggies or other larger foods and let them nibble it. Soon enough they'll eat from your fingers.

If your goldfish eat from the surface just put your finger a bit in the water and the fish nibble on it!

Don't feel bad if you can't get them to that point, though.  I tried with my favorite fish, but he was just not a cuddly guy.  He likes me at the glass, likes my voice, and even waves to me, but eating from my hand and petting are not his cup of fish flakes.  It's individual personality- some fish are more "snuggly" than others.

I coming on this forum and reading other people's excitement and love for their goldfish.  I love my goldfish and really enjoy them everyday.  Best of luck taming your little guys! I havent reached that stage with mine yet either

When you get a new goldfish, it can take anywhere from 2 days to a little over a week to have them eat out of your hand. Some clue in right away and figure out that the most grub is between the fingers...they will make little dashes at the food, then chicken out and dart off, only to return a few minutes later and snag the whole clump! You can gradually move the food up between your fingers and closer to your hand. When they adjust to having your whole hand in the tank, they will no longer be afraid but will boldly nibble it to see if they can  find a morsel. At this point it is not hard to pet them, some will slalom through your fingers and you can rub them.

I would add that I've heard you shouldn't pet them too much though. It's not super great for their slime coat. 

Sometimes when I hold my hand over the water they try to junp out to bite it! 

Ok good to know thanks a ton....I do not want to hurt my little guys.

...And yet, they say a goldfish's memory is only 5 seconds.  Mine always gather in a little mob in the corner every evening at dinner time. They know right where the food is and they DO remember. 

yeah thats a myth and total **** (you know what), Ive heard that said about all sorts of animals and birds as well...

My fish are pretty special, but they can't limbo...

Goldfish can also distinguish between different people...they go crazy when I walk in the room (as I am Food Provider) but don't react with as much enthusiasm when a family member or a friend comes near the tank. 

Their different personalities are cool.  My fish get excited with any attention from anyone even people they haven't seen before, even tho I'm the only one who feeds them. 

It amazes me that they don't care what color I'm wearing, or if my hair is down or in a pony tail, they still love to see me.

I'm glad for this thread.  I'm going to try some hand feeding.  They definitely know the food comes from my hand, 'cuz when I'm putting food in and if it sticks to my fingers, they can't wait and are practically jumping at my hand to get the food, and I'm telling them to hold on a minute...  This sounds like a perfect opportunity for training them.

I don't want to pet them, but to have them swim thru my hand or fingers would be great.

Goldfish deffinately have a begging ritual...the classic wriggling back and forth in one spot of the tank while pumping the mouth open and close. Sometimes they will swim back and forth at top speed from one side of the tank to the other as well. It's funny how they all try to push each other out of the way to get to the food! Waggle your fingers in front of them, and they will immediately go absolutely bonkers! 

Wish I knew how to teach mine some tricks; it would be fun. Anyone have experience with this?

Smart little buggers! 

I know what you mean about the food, Nossie. Would hate to be the size of a pellet in a tank full of hungry goldies!

Aww! Mine do that too

I saw that one fantailer! Lol 

I think if they had kept at it even longer they could have found out how sweet each one could be. 

I haven't ever used an automatic fish-feeder actually... But then again, I don't go away for longer than a week, max! (Especially now that I finally have a car available so I can go home and take care of my babies <3)
So I actually don't know... however, my sister and mother etc, haven't ever fed them but they still come to the glass to have a look for potential treats
Besides, they're probably so used to you anyway that they love you too much to forget

It'd be interesting if someone who actually uses those would have some experience and make a little input, it's an interesting question