I fear you have to rake the stones by hand, pick them up and remove them. Save them though, because they will make good hardcore for paths. Also you will probably find that when you have picked them all up a fresh crop will appear. I have never understood how gardens do this.

If the garden is too big for this to be practical in time for planting you could try broadcasting hardy annual seeds so that something is actually growing on the parts you haven't got round to. Then you can dig them in in the autumn. Or you can plant potatoes on the ground that's still stony, and pick off stones as they appear when you earth up the potatoes - this is anyway a good thing to do with newly turned ground. It is in any case a good idea not to be in too much of a hurry with a new garden design as ideas develop as you live with the site.

Good luck with your new garden and I hope you have many years pleasure from it.

I learned about the stones in geology class:
Wherever the soil freezes in winter, extra ice forms under the stones, and forces them upward through the soil. When the ice melts in the spring, enough soil washes under the rock to keep it up.
It's just a fraction of a centimeter every year, but enough that farmers joke about the good crop of rocks they got, this spring. : )