There are a bunch of things that you can regrow or germinate (grow from seed)!
For example, I have regrown celery, leeks, green onion, sweet potato, garlic and ginger.
For celery, leeks and green onion:
You can cut an inch from the bottom and then set the bottom parts in water, near a sunny window until roots start to grow. After the roots have established themselves then you can plant them in dirt,
For sweet potato that has started to bud:
Just cut it in half, put tooth picks in the sides and then put the bottom cut part in water. Set near a sunny water until the vines start to grow (the vines are edible). Plant in a large container about 15 gallons. It takes about a year for sweet potatoes to grow.
For garlic that has started to sprout:
Just plant separate cloves in a container with soil. After a week or two the garlic plant will start to emerge. You can eat the green part like chives (they taste like garlic). I haven't actually regrown garlic cloves yet but its the same method but you only put one garlic clove in a container as opposed to many.
Fresh Ginger:
Cut the ginger eye bud. Soak in water overnight. Place the ginger root with the eye bud pointing up and cover it with 1-2 inches more of soil in a container. Water lightly. It take a month or two to sprout.
I can do How to's for these 
I have not germinated apple seeds before but I'm sure it is the same for all fruit seeds. The best thing to do is put them on a wet paper towel and place that into a plastic bag. Set near a window. After a few weeks check to see if the seeds have sprouted. Plant in soil in a container. Water.