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.