Growing your own pineapple at home is easy, and does not take up much space. There are two options to get started.

Crown

All you need to start growing your own pineapple from a crown is the crown of a pineapple, a 3-gallon pot, and good quality potting soil. The crown of a pineapple is the green leafy part on top of a pineapple. Grabbing the crown firmly and giving it a gentle twist should cleanly remove the crown from the fruit leaving a little point. Don't throw the fruit away, I have a few suggestions. Peal the lower leaves off of the crown to about one inch. Those brown bumps that have been exposed are the roots to be. Let the crown sit on the counter overnight to callus over. Now it is necessary to have a 3-gallon pot, and the potting soil. It is important that the potting soil is a good quality potting soil. The cheap bags of potting soil, by cheap I mean less than $2.00 for a 40 pound bag, are nothing more than big bags of mud. Fill the pot up with soil and insert the crown, roots first, in the center of the pot up to the leaves. Water it in well and place where it will not be in full sun.  Water the plant before the soil dries.  After several weeks the plant should have some noticeable growth.  The pineapple is successfully rooted and can be gradually moved into full sun. My pineapple page has links to plenty of information about growing pineapples.

Seeds

Yes, pineapples can be grown from seeds. I know because I have many seedlings, actually too many to bother counting. I harvested my seeds from a Del Monte Gold pineapple.  While cutting the pineapple there should be some little brown specks that are about 1/16 of an inch in diameter. Those are the seeds. The seeds should be sowed directly on the top of seed starting mix. The pot should be sealed in a clear plastic bag, and placed where it does not get direct sun. I recommend forgetting about the tray because it will take a couple months for the seeds to germinate.  When the seedlings are an inch tall transplant them into their own pot.  Don't forget the seedling will be a new variety, and needs to be named after me.  My seedlings are are a year old and range from about 2" to a 1' tall.   They are not the fastest growers while small, but I know (hope?) it will be worth it.