When fruit is dropping and birds are feeding in the tree, chances are you're approaching harvest time for that crop. Then apply the taste test. These are perhaps the easiest ways to determine harvest time in the School Orchard, with its multiple varieties of trees.
B - "More in Depth"
For the Apples, you should be able to indent the skin and flesh with your finger nail, and when you cut it open the seeds should be dark brown or black. If seeds are still light color, you're not quite ready for harvest. If there is good sunlight on the apple, and the nights are cold, some red color will still develop.
Be careful when harvesting the Apple! Lift it with a little twist. It should separate at the stems abscission zone (that's the little wider area near the tree end of the stem). If it doesn't come away easily... leave it on the tree. The risk is breaking the little gnarled "Fruiting Spur." In Apples, the Fruiting Spur should bear fruit for 10 or more years. Some instruction for the students and helpers will keep your Apple tree bearing for years, otherwise you'll have to wait for another Spur to develop! Apples ripened on the tree taste great. Let the students have a harvest party, and eat the apples right there.
"Asian Pears" (e.g. Chojuro, Shinseiki) can be harvested like the Apples, and eaten right off the tree. Use the same "ripeness" criteria. They will usually turn from green to a yellow buff color, even almost tan to russet. And for Pears.... treat the Spurs the same as Apples. They wont last quite as long, but they set fruit at the same spot year after year. The most frequent harvest problem in the School Orchard is that kids pick the fruit prematurely, and "pull" the apple or pear down, breaking the Spur.
"European" Pears (e.g. Bartlett) can be picked when they are full sized, but still green and firm. They should then be stored in a refrigerator for at least a week, then taken out and allowed to ripen. These are not eaten "tree ripe." When ripened on the tree, they tend to get "mealy."
Your Stone fruit (Peaches, Plums etc.) are probably all harvested by now, but if not, they should be allowed to ripen (soften) on the tree and eaten fresh. The Persimmons should be ready from October to November, in most regions. Both common varieties should be bright, shiny Orange in color. The flat, squat shaped ones, the "Fuyu," should be eaten when they are firm, like an apple. The acorn shaped "Hachiya" must be almost custard soft before you give them a bite! (but they can ripen off the tree) If you mix the two up you're in for a mouth puckering surprise! Persimmons should be harvested by cutting the stem (there are harvest clippers that are shaped like your two fingers when you make a cutting sign.