How to get from the wavefunction to weighted states?

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I Have a question about how we arrive at the probabilities for the wavefunction collapsing to some specific value for an observable.

As far as I'm aware, the wavefunction is a superposition of possible states depending on the observable we try to measure.
Lets say I want to measure observable A,

What is the procedure for getting from the wavefunction to a set of possible outcomes with coefficients that weight the possibilities?

Apologies if the question isn't well formulated.
thanks in advance.
 
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