I agree with Anne, don't cut the seed. You can also start it in water by suspending the seed over a jar with toothpicks. Or my mom let me use a tapered wine glass, but you must keep the bottom of the seed touching the water. Once it starts growing roots and making a shoot out the top (pointy end of the seed) you can then plant it.
Not to discourage you, it's a fun project to grow them from seed. But it will take you probably 8 years to grow a tree big enough to bear fruit from a seed. Then what you get will not necessarily be the variety that the seed came from because they are wind-pollinated, so a different tree in your neighbor's yard could have pollinated it, making it a cross.
If you really want to grow your own avocado tree for the fruit, go to a good nursery (not Home Depot or Lowe's or Wal-Mart!) and buy a little grafted tree of a good variety. You will then get the fruit you want in maybe 3 years.
Mango can be started from seed the same way, or set the seed on its edge in some potting soil. Same cautions apply, though. Takes years to grow a tree big enough to get fruit.
