Tangerine seeds are easy to get--just pick them out from the fruit as you eat--and easy to plant. The resulting trees probably won't ever bear fruit if grown indoors, but they make an attractive houseplant nonetheless--and one can always hope. Planting fruit seeds is also an excellent way of educating young children about how seeds germinate, how plants in general grow, and where fruit comes from.
Remove the tangerine seed or seeds from the fruit as you eat it. Immediately place them in a small bowl filled with lukewarm water.
Leave the seeds to soak overnight. In the morning, rinse them off in more lukewarm water.
Plant the tangerine seeds 1/2-inch deep in moist all-purpose potting soil with an aerating agent, like perlite, mixed in to help it drain quickly and evenly. Plant two or three seeds in the center of each pot. If more than one seed sprouts, you'll pinch back all but the most vigorous of the shoots.
Cover the pot with a piece of clear plastic wrap--make sure there is at least 1 inch of air space between the wrap and the soil--and place the pot in a warm, bright, sunny window.
Wait for the seeds to sprout--this may take a few weeks. Check for signs of growth above the soil, but don't disturb the dirt itself, every day. Keep the soil beneath the plastic moist but not soggy.
Remove the plastic once the seeds sprout, and keep your mini tangerine plant in the same warm, bright, sunny window.