I've recently started a few attempts at growing fruit, or at least plants, from the seeds of fruit bought at the supermarket. Leslie Gadallah has an interesting article on the subject. Each fruit and seed requires its own procedure: Peaches for example, take a very long time to germinate. Lee Reich recommends leaving the seeds in the fridge for several months. But first you have to open the hull, which is extremely tough. I've already ruined a nut-cracker, and saw one video were a vice was used.
Avocados on the other hand are easier to sprout. Here's three different ways, with more details on the planting. Here's a slightly different method of filling of up with soil. In my experiment, I don't have much to show for yet, and might even have to try again with another seed.
With pineapple, there are two different ways to grow a new plant. First, you can pull off the leaves on the top, leave in water then plant. Secondly, you can collect the small seeds inside the fruit. Again, I don't have much to show for just yet, but I did plant the top part which was showing signs off roots after being in water for about two weeks.
Finally, I've tried mango seeds, and that's a success so far. Carefully opening up the husk inside the fruit, and leaving the seed in a moist zip-lock bag for a few weeks. You can even grow multiple plants from the same seed. Here I just planted my first seed, which already has a few leaves, as seen in the picture below.