The most certain way to know when to pick apples is to pick one and taste it! The fruit should have developed a good color for the variety. Some are deep red, others are red with a yellow background, and yet others mature to yellow or green. Get to know the characteristics of the varieties you are growing. Mature fruits will have dark brown seeds. Cut through the core to check this. Apples will also ripen off the tree, but not if picked too green.
If you plan to store the fruit for a long time, pick the fruit slightly on the green side, because it will continue to ripen a bit after harvest. However, for best flavor allow the fruit to ripen on the tree. Keep in mind that fruit on a single tree may ripen over a couple of weeks. Fruits exposed to full sun at branch tips often ripen earlier than those hidden deep in the foliage. You may need to harvest several times to catch all fruits at their prime.