Wash the glass canning jars and lid rings in hot, soapy water or a dishwasher. Keep the jars in the dishwasher on a heated dry cycle or in hot water until ready to use to keep the jars sterilized.
Remove the grapes from the vine and wash them by placing them in a large bowl and running under cool water. Crush the grapes with a potato masher or place them in a food processor for several seconds. This will release the juice for processing.
Mix one box of jelly pectin with 1/4 cup of sugar to prevent the pectin from clumping when added to the grape juice. Measure out the amount of sugar needed to make one batch of grape jelly. The amount is usually 7 cups of sugar for each batch that requires 5 cups grape juice; however, verify the correct amount inside the pectin box.
Place the crushed grapes in a kettle and bring the contents to a boil to assist with releasing the juice. Let the grapes simmer for 10 minutes. Strain the heated grapes with a jelly strainer or with a layer of cheesecloth placed in a colander. Pour the grapes into the strainer to separate the juice from the grape pieces.
Pour the grape juice into a clean kettle and in the pectin-and-sugar mixture. Heat the juice to a boil while stirring regularly to prevent the juice from burning. Boil the canning lids in a pot of water while the grape juice is coming to a boil.
Add the sugar to the juice and pectin once the mixture comes to a boil. Bring the mixture back to a hard boil and let it boil for one minute while stirring regularly.
Test the mixture's jell by running a metal spoon under cold water and then taking a spoonful of the liquid mixture. If the liquid turns into a jelly consistency, then it is ready to process into jars. Add another 1/4 box of pectin if it remains in liquid form and boil for one minute.
Fill the glass jars with the jelly liquid to 1/4 inch from the top of the jar. Wipe the top of the jar to remove any spilled liquid, set the hot lid on top and screw the lid ring over top until it is tight.
Place the jelly jars into a canner filled with boiling water making sure there is at least 2 inches of water over top of the lids. Boil the jars for five minutes to seal the lids. Verify the boiling time in the jelly pectin instructions as this may vary depending on your location's altitude.
Remove the jars from boiling water canner once the time is up. Place the jars in a draft-free area for 24 hours, making sure they do not bump into each other while they are hot as this may cause them to break.
Press the top of each jar to make sure they are sealed. If the lid pops up and down, it did not seal and needs immediate refrigeration to prevent spoilage.