Wash your canning jars, along with their lids and screw bands, in very hot, soapy water. Rinse well and let them air dry. Check for cracks and chips before using.
Rinse the fruit. Remove skins, stems, and peels, and quarter the fruit if necessary. Toss it with the sugar and refrigerate the mixture overnight.
Put the teaspoon in the freezer. Put the fruit mixture in a large, heavy-bottomed saucepan, bring it to a low boil, lower the heat, and let it simmer until it thickens and becomes syrupy. This will take anywhere from five to 20 minutes, depending on the kind of fruit you use.
As the fruit is simmering, sterilize the jars and lids according to the canner's instructions. Leave them submerged in the hot water until they're ready to be filled.
Remove the sterilized jars from the canner with a jar lifter or stainless-steel tongs and place them on clean dish towels. Drain them upside down for one minute. Then, ladle the hot fruit mixture into the jars, leaving a quarter-inch space on top and taking care not to splash any on the sealing area. Wipe the rims with a clean, damp cloth, and then screw on the lids.
Carefully lower the jars into your canner. Add enough water to fill the pot two inches above the jars and cover. When the water comes to a boil, let them boil for 10 minutes. If the water level hits the top of the jars, add more boiling water.
Turn off the heat and remove the canner lid. Wait five minutes, then remove the jars carefully using the jar lifter or tongs. Let them cool on a towel, spaced at least one inch apart, for 24 hours. Don't attempt to retighten the jars.
When the jars are cool, make sure they're correctly sealed by looking for a slight indentation in the lid. If any did not seal properly, refrigerate them and eat the jam within two weeks. Wash the outside of the other jars and store in a cool, dry place, out of direct light. They'll keep for about six months.