This page explains how to obtain the golden shovel, which lets you bury certain types of items in the ground that you can't bury with the regular shovel.
A golden shovel, unlike the regular shovel, has a powerful special ability. The golden shovel will allow you to bury bags of money in holes that you dig in the ground. You can bury any sized bag of money with the golden shovel. Dragging the stylus from your money bag in your pocket view will prompt you to choose an amount ofmoney to put in a bag. A bag of money that you bury will turn into a tree, and there is a possibility that the tree will have money bags growing on it! The larger the amount of money that you bury, the more likely it is that you will grow a money tree. See the (not yet written) money tree guide for more information.
The first step to getting a golden shovel is to have two shovels. Yeah, it seems like maybe it is kind of a waste to have to buy two shovels to get one golden shovel, but I have never figured out any way to get the golden shovel without using a second shovel. I guess you could have a friend with a shovel come to visit your town and help you out. But, really, at that point, you are kind of putting a little too much effort into getting a golden shovel, maybe.
You need to go to Tom Nook's store to buy shovels. That is the only place where you can buy shovels. Tom Nook always sells tools, but he might not have a shovel in stock every day. The tool selection in Tom Nook's shop changes each day, so just keep on checking Tom Nook's shop for shovels, and buy one if you do not yet have two shovels. Once you have two shovels, you are ready to move on to the next step.
The next step in getting a golden shovel is to bury one of your shovels under the ground. You could theoretically do this step without having two shovels, because there are occasionally Pitfall Seeds buried in town, which will make a hole if you or a villager steps on it. So if you walk on a pitfall seed, you would create a hole, and then you could just walk up to the hole and go into your pockets and tap on a shovel, and you would have the option of burying it. But then you would need to kick the dirt over the shovel, and you would not have a way of opening up that hole again. You would need a shovel to do it.
So, anyway, using one of your shovels, dig a hole in the ground, anywhere you like. As mentioned in the paragraph before this one, you also have the option of walking on top of a buried pitfall seed and jumping out of the hole and using that to bury your shovel, or waiting for a villager to fall into a pitfall and using that as the hole. Whichever method you use for digging the hole, it is a good idea to bury your shovel in a place where you will remember where it is. You do not need to water it after burying it. Just leave it there.
Now, all you need to do is wait a full day (24 hours), leaving the shovel buried underground. Then, after it has been 24 hours, you can go ahead and use your second shovel to dig up the buried one. If you left the shovel underground for at least 24 hours, the shovel that you dig up will have transformed into a golden shovel. How does the shovel turn golden just by being buried? Who knows. I guess the very ground in your Animal Crossing: Wild World town has magic powers. Or something.