First you have to decide what kind of peaches you want to can. For years and years I have taken the advice of the silver haired ladies at the farm stand and canned Lemon Elberta. Their advantage is that they are very big and firm. They peel really easy, and they hold up really good in the jar. The disadvantage is they aren't as sweet and peach tasting. This year I tried a some Pink Ladies, and they are sweeter and more peachy indeed, however, they are more susceptible to mushy stringiness. I won't be able to tell you what I prefer until I crack a jar open in the dead of winter with some cottage cheese. If it is your first time canning peaches, I recommend the Lemon Elberta. One box (half bushel) will do between 12-14 quart jars.
First prep your jars, the best way is to put them in the dishwasher, that way they will be clean and hot and ready to go. If your jars are clean and you don't want to wait a whole dish washing cycle, just rinse them with hot water and you will be fine. (the canning nazi's would probably disagree). Meanwhile, get a big pot of water boiling to blanch the peaches. Also get your canning pot boiling.
Get out three big bowls, (or you could use your double sinks, I have a farmers sink so it doesn't work) and fill them with cold water. One pot is to drop the blanched peaches into, the second is to drop the peeled peaches into, and the third is to drop the sliced peaches into. In the second two pots, add a few splashes of bottled lemon juice that way the peaches won't go brown. Boil a little water to soak the canning lids in as well.
Next, prepare the syrup that will go in the jars with the peaches. I do a medium to light syrup. I looked up the instructions for syrup that Ball gives and they were needlessly complicated. A med-light syrup is plenty sweet and if you want anything else, look another place. I do a simple ratio of 2 to 1. Two cups water for one cup of syrup. I did 27 quart jars of peaches today (one bushel), and used roughly 9 cups of sugar (18 c water).
Blanch the peaches in boiling water for about 60 seconds, till skin comes off easily (don't cook too long or you will get mushy peaches). Drop into cold water.
Peel the skin off the peach. The skin should just slip off the peach. I just let the skins build up in the very bowl I drop the peaches into from the hot water. Once they are peeled, drop them into a different bowl of cold water (that has lemon juice in it).
Slice the peaches into the third bowl with cold water. You can do halves, slices or quarters. I do quarters. I like halves, but you can't fit as many into a jar. So quarters is a compromise.
Drop the sliced peaches into the clean warm jars. Give the jar a shake so the peaches can work their way comfortably to their place. You want to fit as much as possible in the jar but below were the jar's lid screws.
Pour the hot syrup into the jar, just to cover the peaches (see the tomatoes to know how full).
Stick a knife or a chop stick into the jar to release any air bubbles.
Wipe the jars rim with a paper towel to make sure its free from anything to prevent it from sealing.
Top the jars with a warm sealing lid, and screw down with a a ring.
Immerse it the boiling water and cover with the lid. Boil for 30 minutes.
Remove the jars from the water and let the jars cool on the counter. They often won't seal till after they have come out of the water. Once they are cooled. Check the seal by pushing on the top. If it still have a flex or a pop, it didn't seal. You can try again, but replace the lid.