I don't know about apples, but I've grown peppers from seeds in the grocery store ones.

I put the seeds in a moist paper towel, inside a tupperware for a few weeks until they sprout (sounds like you can skip this step). Then I plant them in planters and see which ones really take (and of course this way I can still have the flexibility of indoor or outdoor depending on weather). Once I have a couple of 2 to 3 inch tall plants, into the ground they go.

Good luck!

While this is a fun experiment, please be aware that, unlike those bell peppers, the offspring you get from these apple seeds is likely to be very different from the parent Gala tree. There will be a wide range of variability in tree size, vigor, fruit size and taste, etc, etc -- unlike a graft, where you know (thanks to vegetative propagation) that what you are getting is a piece of the original Gala tree, with all its known qualities, attached to a known rootstock with the attributes that confers. And it will take you many years to find out what your new seedlings' fruit will be like.

That said, you can plant them in good soil in a large pot, then move them out into the ground when they get a little size on them -- best way I know of to keep them from getting accidently mown down or trodden on.

Enjoy! You could be harboring the next Granny Smith! I understand that came from a seedling sprouted out of a compost heap, if that isn't a myth...

LynnT

My grandfather used to plant the seeds from things - apples included. He got some very nice plants that way including a super apple variety I wish I could find again.