First of all: Keep calm. If you are too eager to capture it you will probably just scare it away. Keep calm and try the following:
Notice: The bird will not know how the outside of your house looks and may not know its way back even if it want to come back, but it is likely to recognize the voice of its mate, any of its friends (if you have several parrots) or you, so continue calling for it. Also it may recognize its own cage if you put it in the garden.
A caged bird is typical not a strong flier so chances are it will be very close to your home – walk around your neighborhood and keep calling for it.
With a little patience there is a good chance that the bird will return when it gets hungry or thirsty or just overwhelmed by this new unknown world.
If it come back and sit on your shoulder or arm do not try to capture or hold the bird as that may scare it away – instead keep talking to it with a calm voice, perhaps give it some treats while you carefully walk back inside the house and close the door.
Notice: Many local communities have a Facebook group – try writing a notice here, maybe somebody in your community has seen your parrot and maybe even caught it already.
Also check out this page: Help! There is a parrot in my garden