Don't think you will need to dig a hole, just place several of the ones that have sprouted in the locations that you want new trees. Clear away the leaves, so that the acorns are in contact with the soil and cover lightly with some of the surrounding soil to retain moisture. Place some protection over them(small wire mesh is good) to prevent squirrels from eating or carring them away. Leave the mesh in place until the acorns have decomposed and they are no longer attractive to the rodents.
After a couple of years, select the more robust seedling and cut off, at ground level, all of the others in the group. The underground stem(root) will be about as long(or sometimes longer) as the above ground portion and are usually tough to pull up. Once you cut it off, the remaining root will die.
Mulch the seedlings to conserve moisture, allowing a gap around the trunk for air circulation. Water weekly, during dry spells. Fertilize using compost or aged manure. If you choose to use a chemical fertilizer, use a timed release type for trees & shrubs and water in well.
White Oaks are the easiest of the Genus to grow from seed, but they are slow growing trees, so be prepared to wait several years to enjoy their shade. They can live to be 400-500 years old, so your descendants will be thankful to you several centuries down the road! :Rb

Thanks, razorback! I knew someone would be able to answer this question. I have a three year old pin oak that came up from seed that is now 8 to l0 feet tall and a tulip poplar that is four years old and at least 15 feet. I know the white oak is slower growing, but it is so magnificent. I have many mature ones on my property, but I lost two due to construction, and these are the ones I want to replace. I can wait and be patient.

I would never have thought of the mesh. That makes good sense. Will get on it right away!

Donna, I have planted many acorns from both white and red oaks. I personally recommend burying the acorns about an inch in the ground. Place just enough soil over them to cover them. Like razorback said, you will need to cage them. If the squirrels don't get them now, the deer will later (when they're saplings).