We can make a simplifying and unsatisfying assumption - the observer has a register in his head which records the result of the measurement. Here, it is easy to imagine this register is part of the wave function just like the object being measured. As mentioned above, the wave function for this register is entangled with the object being measured so the measurement and register value are correlated. In our model this corresponds to the person independently thinking each of the possible results, which some people call multiple universes.
But this simple register is not what goes on inside the brain. Not knowing this makes it difficult to accurately model the measurement process.
EDIT: for clarity
Granted his quote used the word formulate, but I interpret the comment as referring to not just writing some rules but also having some justification for them.