You need 2 things, your ID # and you SID (Secret ID #) your secret ID is hidden from you within the game. The only way to get it is to have caught a shiny pokemon within game (not chained, just a random shiny you came across) or use AR to find it for you. This is the only thing you'd need AR to do, and because I don't have one and never will I found a friend who got a friend with AR to help me.
You plug that into the program, next go somewhere where you can catch lv. 50+ pokemon, I use the Resort Area's Pond and fish for Magikarp. Then switch your poketch app to #5, that's the one where you see your party. Make sure you only have 5 pokemon no more or less with you at this point. Save the game. Reset. Take note of the time you hit 'A' on the continue screen, so if you did it a 5:18 pm, you would plug in, 17:18. Catch a 50+ pokemon, then put in its stats and natures into the program.
Then it will calculate how many taps and flips you need to do. (If you have international parents you must say so, if not then you have to select normal on the program.) This means you switch to app #6 the happiness checker, if the program says 106 happiness taps, you tap it 106 times. Then if it says 6 flips, you do the coin toss 6 times.
Then put in 2 compatible pokemon in daycare, get the egg, hatch, ta dah, its a shiny ~