Planting papaya is relatively easy... buy a papaya from the shop, see if you like it - if you do - then scoop out all the seeds from the center of the papaya. These aren't actually the seeds - the seeds are within them - these are essentially juice sacks encasing the seed itself.
Place these juice sacks-cum-seeds between a folded peice of newspaper and roll them with your hand till you pop the juice sacks - open the news paper and you will see smaller black coloured seed kernel - these are the actual seeds - clean them up and place aside on a dry paper, preferably in the sun, for at least a week. After this, they are good to use for planting and can be kept for almost a year!
When planting, choose a location and scatter some of the seeds in that spot. Choose some more spots similarly and scatter seeds in each of the spots. Scatter/sprinkle a few (10?) in each spot - not just one. Not all seeds may germinate - so you want to provide some extra. Cover the seeds with some mud/compost/mulch.
From those that germinate (which may take a couple of weeks) - see which ones are doing better and pull out those that don't look strong.
As they grow, you will have to see whether its a male or female papaya plant that you have got. Males don't give fruit - so you want to have a lot of females with maybe one male for every 15 females. You will be able to make out this by looking at the flower - the male will normally have long thin stalks coming out with flowers at the end of it whereas the females will have flowers right at the trunk of the plant itself.
Hope to try this soon!