If you've collected beech nuts from your tree there's a fair chance that some, or most, of them will give you a copper beech, though some may turn out green.

First, give your nuts a squeeze (😉) to check that they are nice and plump. You may find a lot of empty ones. Now for the hard bit. Beech seeds must be stratified, in other words they have to think they've been through a winter before they'll germinate. Sow two or three in three-inch pots in well-drained compost (add a bit of sharp sand or something, leaf mould if you make it) and leave them outside for the winter. You will have to fiercely protect them from birds, mice and squirrels. Maybe put them in a shed or outdoor garden store and keep an eye on them for getting too dry, but those BLOODY mice...In the spring make sure they don't dry out. Your success rate may still be quite low. Another thing you can do is to put some seeds in little plastic bags of dry but not bone-dry compost and put them in your fridge for the winter, then sow them in late Feb or March in pots outdoors. Don't expect fast germination. Just leave them, for months if necessary. I'm trying this with stone pine seeds that I bought in Madeira. They are in the fridge for a few more weeks yet. Good luck!