I have a young apple tree (Spartan) with a small number of nice sized apples.
How can I tell if they are ready to harvest?
I am currently harvesting some of mine. I support the apple in the palm of my hand and give it a slight twist; if the apple is ready to harvest, it will separate easily from the spur.
Those that are not quite ready for harvesting often ripen very quickly, so it is a good idea to check the ground below the tree every couple of days, to collect up any windfalls before they start to rot.
If you had a large number and were more used to the tree, I'd suggest simply tasting the apples to see if they were ready to your liking (some like an apple that's more tart).
Since you have a small number, you might consider a few options:
This link provides a guide for most common fruits.
If the apples are close to ripe when you pick them but not quite, they will still ripen a bit off the tree. So all is not lost if you pick an apple that's not quite ripe.
I've actually heard that Pink Lady apples (a very late variety) are often picked early and allowed to ripen in storage in cooler climates. I'd imagine that a tree-ripened fruit would win out in taste tests though.