A year ago I brought two completely terrified, unsocialized Senegals who screamed and shook in their cage when any human was within sight. A year later they are both friendly and step up onto an out streched arm when asked. The male lets me stroke his beak and scape stuck food pieces off it, and the female of these two even lets me put my hand around her and itch her head and neck with my thumb.
To get this close you need to start off with the easiest part which is the beak (others have said the toes but mine still aren't keen on having their toes touched, plus it's much easier to get bit if you touch the toes).
To start, choose a phrase like 'Can I touch your beak?' and use that phrase everytime before you try to touch your bird's beak so it knows what you're going to do.
When touching the beak, touch your index finger to the top part of the beak (the only place they can't bite you from) if he opens his beak in anger just say 'Ay!' and then go straight back to touching the beak, (the first time) try to touch the beak twice, say good bird and then leave it. The next time try to touch the beak three times and then just keep on building with that until the bird no longer seems bothered by having it's beak touched.
After that either try touching the bird's head: Make sure the bird is lower than your neck, touch the birds beak and slowly move your hand further forward, towards the top of the head (the bird needs to be lower than you so that it's easier to pull your hand back if it tries to bite).
Or touching the birds wings: Try to get the bird standing on a shelf or flat area (if it's perched it may be too worried about you accidentally knocking it off), ask 'Can I touch your wing?' And then try to touch the side of the wing, say good bird after you've finally managed to touch the wing unscathed. Slowly try to get the touch to last longer until the bird will happily let you hold your hand against it's wing for at least 15 seconds.
After getting through these three steps, getting the bird to let you touch it's head and back shouldn't be too difficult, just keep going slow and make sure it always ends on a good note, with enough persstance it shouldn't take longer than 2 to 3 weeks.
Hope it works out,

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P.S, Try to make sure the parrot can't fly over your head, I had a bird try to fly over and away from me, it used one of it's claws to grab the top of my eyelid aso it could get itself more lift (pain).