If a quantum particle/system has not been measured/observed yet, how can you know it is in several places/states at the same time?
Weak measurements allow you to find out stuff without causing the collapse of the wavefunction.
In quantum mechanics (and computation & information), weak measurements are a type of quantum measurement that results in an observer obtaining very little information about the system on average, but also disturbs the state very little.
On a side note, I don't believe it's common to say that the body's in several states at once: it's better to say that it's described by a single linear superposition state.
If a quantum particle/system has not been measured/observed yet,
In quantum mechanics models, the only deterministic solutions are the moduli of the wavefunctions , and what these moduli determine is the probability distribution of measuring a particle at (x,y,z,t) or with specific energy momentum fourvector. If you have modeled your system well, that is the only "know" you have.
how can you know it is in several places/states at the same time?
A particle or a system when measured give one instance in the probability distribution, and it will need many measurements to validate the distribution and be sure the model is correct. One measurement will not do it, because the system will be in one of the allowed locations by the predicted probability distribution.
Here is an experiment with a simple system : " one electron at a time scattering on two slits of specific width and distance apart"
Each individual electron materializes at the $(x,y,z_0)$ of the screen at different times from the others. It leaves a footprint of a point particle. It is not spread all over the available phase space. At the top, the footprints look random and countable. Accumulating many electrons illustrates the build up of the probability distribution, and lo, an interference pattern appears. This validates that the electron is a quantum mechanical entity, described by a wavefunction solution of the Dirac equation, and the specific accumulation of points builds up the probability distribution expected from interactions of quantum mechanical entities.
That is the only thing we can "know" of quantum mechanical entities. The mathematics used to model the behavior of quantum mechanical systems should not be taken as describing mass and energy distribution spreads , because experiments show that they do not.(There is no measurement of spread out single electrons).