Unfortunately a muon created as a result of Cosmic Rays is not easily seen, but their after-effects when passing through is a little more easier, typically most forms of radiation detectors will do the job. The oldest and most famous example of this is the Cloud chamber. There is an operational cloud chamber installed and running at the South Australian Museum and is well worth a look (I think its fascinating).
The problem using a radiation detector for a cosmic ray observation is that there is larger amounts of terrestrial radiation as much 73% of background radiation is due to the natural decay of matter. Although in small quantities it is sufficient to make it difficult to discriminate between a terrestrial or cosmic source.
Consequently at least two detectors are needed placed one above the other, feed into electronics that can monitor coincidence between the two detectors quickly thus potentially filtering out most terrestrial radiation.
Cosmic particles travel at nearly the speed of light and so do not ionise very efficiently and hence can travel through matter very easily passing through both detectors without effort, whereas the terrestrial radiation may not. Consequently anything detected in both detectors simultaneously is more likely to be a cosmic event than terrestrial.
Well almost simultaneously, if a muon is travelling at 0.998c and the detectors where spaced 5cm apart the actual flight time of a muon would be just 0.16ns. However as the detector and electronics response and delay times would be much slower than this, we can say in "real-life" terms it is simultaneous.
The main idea of coincidence detection in signal processing is that if a detector detects a signal pulse in the midst of random noise pulses inherent in the detector, there is a certain probability, p, that the detected pulse is actually a noise pulse. But if two detectors detect the signal pulse simultaneously, the probability that it is a noise pulse in the detectors is p2. Suppose p = 0.1. Then p2 = 0.01. Thus the chance of a false detection is reduced by the use of coincidence detection.