First of all, the uncertainty principle and observer effects are completely irrelevant. The tracking devices in modern detectors are large enough to be firmly in the realm of classical physics. Any uncertainty in the detector's wavefunction is negligible compared to the size and energy of the device itself, and the effect of detected particles on the tracker is not more than the loss of a few electrons here and there. Granted, over trillions of collisions, this could become a problem, but trackers are built to resist this kind of damage. They have electrical connections to replenish lost electrons, and they are made of dense materials that will retain their structure even if the occasional atomic nucleus gets transmuted into another one due to radiation.
As for how these tracking devices actually work: there are several different types. Each of them records a particular type of information, and is sensitive to only certain particles. The trackers are arranged around the beamline (the path through the center of the detector, where the incoming particles go) in a way that allows scientists to identify the signature of a particular particle by cross-checking the outputs of different types of trackers. It looks basically like this picture, from Wikipedia:
(that's the ATLAS detector).
A typical detector includes the following types of components, working from the inside out:
A silicon tracker consists of small "panels" of silicon arranged in concentric layers around the beamline. A charged particle produced in a collision will pass through one of these panels and knock a few electrons off the conduction band of the silicon (via the electromagnetic interaction), creating an electrical signal. Each panel is connected to its own dedicated wire, and the other end of that wire runs to the detector's readout circuit (an interface between the detector itself and the CERN computers), so the computer knows exactly which panels were exposed to outgoing particles, and to some extent, how much.
Silicon trackers don't measure the momentum of a particle, but they don't change it very much either. They're more focused on accurately measuring position. Since the individual silicon panels are quite small - maybe a few centimeters on a side - the computer gets access to precise information about the location of the particle as it passed through this tracker. And with six or seven concentric layers of silicon, spaced a few centimeters apart, you can reconstruct the path of the particle pretty well. You can see a visualization of the information received from the silicon tracker in the center of this image from CMS, the red blocks in the middle:
At this stage, it's impossible to know what kind of particle the tracker is seeing, but only charged particles interact with the silicon, so anything that leaves a track has to be charged: probably an electron, muon, or light hadron.
Next up are the calorimeters, which are massive blocks of metal designed to absorb certain particles and measure their energies and momenta. There are usually two kinds: electromagnetic calorimeters, which absorb light particles that interact electromagnetically (electrons, and photons), and hadronic calorimeters, which absorb particles that interact via the strong force (almost everything else).
Calorimeters are shaped into thin "wedges" that are pointed toward the interaction point, as you can kind of see from the first picture on this page (see the yellow layer). Each particle deposits its energy into one wedge of the calorimeter, corresponding to the direction in which it exited the silicon tracker. But the calorimeters don't detect individual particles; they can only identify how much energy was deposited into a particular wedge, and thereby get a distribution of the directions in which energy came out of the collision. The amount of energy deposited can be determined by measuring how hard the cooling system has to work to maintain the calorimeter at a constant temperature.
If you were to look at the data collected by the calorimeters only, you'd get something like the yellow blocks in this image:
Outside the calorimeters, modern detectors include a muon spectrometer, which operates a bit like the silicon tracker but on a much larger scale, using crossed strips of metal instead of silicon. The muon spectrometer records the tracks of muons by checking which strips receive electrical signals as the muons pass through them, and it can determine their momenta because the entire detector is inside a magnetic field, which makes the muons' paths curve. The radius of curvature tells you how much momentum the particle had.
At this point, everything except neutrinos has been detected, and there's nothing you can do about the neutrinos, so we just let them go.
As I mentioned before, the electrical signals from the components get fed into readout circuits, which convert them into digital signals that are then passed on to the computer. A detector sees thousands of collisions per second and collects an enormous amount of data on each one, so it can't all be stored. Instead, the signals get sent through several levels of triggering systems. The first level simply combines the readings from different parts of the detector and throws out any detections which are "boring" - for example, none of the trackers got any readings, or the readings don't exceed a certain threshold, or whatever the detector team decides is not important. (They go through a long process of analysis to decide what is not important.) After that, anything which hasn't been eliminated is sent to the CERN computer cluster for a more sophisticated analysis. What comes out at the end are sets of numbers giving the signal strength measured by each of the detector components, but only when all those signal strengths together constitute an interesting event.
If you have access to these signal strengths, you can feed them into a computer program which will produce an image of the detector and plot the corresponding signals on top of it. That's where the particle traces you've seen come from: the detector press team (or others who have access to these raw measurements) will pull out the best-looking ones and release computer-generated "pictures" that show the measurements.