How can we "know" that system interacted with another system or environment in quantum mechanics/decoherence? I might be raising measurement problem in quantum physics in different words, but I will ask the question.
Quantum decoherence has been proposed by proponents as a theory that eliminates all weird issues involving quantum mechanics, such as Schrodinger's cats and measurement problem.
So in quantum decoherence theory, system (example: a particle) becomes "measurable" when system interacts with another system or environment with certain conditions and consequences.
But this seems to raise issues of how systems can ever be interacting "objectively". After all, every system described by wavefunctions that only give probability for possible measurements in general (of course there are cases that when met with proper basis and knowledge of wavefunction, definitive measurement can be guaranteed). This for me seems to suggest even before quantum decoherence, two systems that will interact have been connected by some wavefunction that describes the chance of quantum decoherence. Or we need some kinds of observers to either bring effects of quantum decoherence.
If the question seems a bit confusing, the context in which the question is being asked is how quantum decoherence theory affects quantum mechanics's measurement problem.  
 A: First of all, it is indeed correct to model decoherence as a system interacting with what is called the "environment". Basically you have a joint CLOSED (unitary) evolution of system+environment, after which you discard the environment (technically called a partial trace), and you are left with the state of the system. Your "observer" can be taken as part of the environment with which the system interacts.
Now, to experimentally detect decoherence, all you have to do is to perform the experiment repeatedly, measure the in various bases, and collect the statistics. At the end of the day you can perform what is called "state tomography", that is, reconstruct the state of the system from your measurement statistics, and there you will see that the off-diagonal elements of the density matrix tend to be small (which is an indication of decoherence). 
In principle, you DON'T want decoherence for micro tasks such as quantum computing. Decoherence is what makes our macroscopic world be as it is, that is, behave classically.
A: A simple answer is that if you have a pure state and it interacts with a system then it entangles with that system. If you measure your quantum system it will not be in a pure state anymore it will be in a mixed state. That is how you will know.
