While fruit that you make into jam and jelly shouldn't be rotten, it can be bruised and squishy. Even overripe is okay. In a home garden it may be tough harvesting enough fruit for preserving in a single day, but over the course of a few days you can collect enough. While the physical quality may not be supreme for older fruit, it can be made into wonderful jellies.
Part of the process of making jelly is to cut and cook the fruit. By the time it has simmered in a pot, all of it is reduced to a slurry that reveals no bruising or unsightly dents, just fruity goodness.
I do both and have favorites. I prefer grape jelly to grape jam, but I like strawberry jam more than strawberry jelly. Rhubarb jelly and elderberry jelly are better than the jams they make while blackberry and raspberry jams are better than their jellies. A lot of it comes down to texture and appearance, but at its core it's all about personal preference and each individual can decide what they prefer.
The process is very basic. Take fruit, add packaged pectin, sugar, and maybe a little lemon juice, heat it in a pot, ladle it into jars, heat the jars, put a lid on the jars, and then store them in the pantry until you're ready to enjoy the delicious results.
Recipes for making jelly should always be used; don't wing it. The Ball company (maker of pectin, jars, and lids) produces the "Ball Blue Book", a great resource that shows you every step in the process and includes many great recipes. It should be a part of every gardener's library.
The reason that approved recipes (approved by the USDA, Extension service, or major manufacturer) should be used is all about food safety. Your grandmother's recipe may taste good, but it may not have enough sugar or acid to keep harmful bacteria out. We've learned a lot about food preservation in recent years and you don't need to worry about harming your family or yourself as long as you follow prescribed methods and formulas.
It helps to see someone else make jelly before you try it for the first time so I've made a video to help. It's a little intimidating the first time you do it but before long you'll become a pro. Making jam as a beginner is a little easier because you don't have the extra step of collecting the juice from the fruit, but both products are easy to make.
If you haven't made jelly before you should try it. If you have, you should keep doing it. While I love my compost pile, I'd rather see delicious fruit in a jelly jar than decomposing on the pile.
Take a look at my video:
GardenerScott's Jelly Video