Adopting a stray cat can be a very simple task. It requires that an amount of food be left outside everynight, on your porch. Usually a secluded or private location for the stray to eat in privacy is warranted, in order to coax the cat into the vicinity comfortably. Upon first sighting of the stray eating or being in the vicinity, cuation needs tobe taken not to frighten it away. Small whispers of typical human - cat interaction are allowable, e.g. calling 'hear, puss puss', crouching to its level etc., but take note not to seem to wanting of the cats attention. Repeated sightings of the cat should not prompt distrust between you and the animal, don't pry upon its feeding area and don't try too hard to approach it.
Once you feel confident that the cat is staying around for the food you leave out, start wheening it off the nightly supper routine and only feed it when you are there. This will need you to have the cat watching while you top up its food dish, the cat will understand that you are feeding it. Once you have topped up the dish, ask it to come and eat calmy, and then leave, still watching the cat (knowing that the cat is being watched), hopefully the cat will approach the food while your are still watching it. If it doesn't you will have to continue to do this until it does approach it's food bowl compfortably while you are around, only then will you be able to finally interact with it one day, as it forgets that you are a foe and it approached the food bowl while your filling it. Again with time you should be able to touch the cat while your filling the food bowl, and again with time should be able to call over the cat, while not at the food bowl. When that happens you could call the cat in question your own.