On my second day up at the summit, we had the opportunity to go into the interferometry lab. It's a veritable playground of optomechanics, as if someone had hopped up a class of 9-year-olds on birthday cake and let them loose in a Newport or New Focus warehouse.
There are many different parts to the lab, so I'll try to walk you through them as I did. The lab itself is more or less in the center of the summit observing platform, with a small building atop it. You enter the lab by going in this building and then down some stairs - the subterranean location helps out with temperature stability.
Also in the outer lab are the controllers for the cryogenic detectors. The computer chips that the starlight falls onto and thereby detect the light do so by measuring electronics jogged loose by that light. However, heat energy will also jog loose electronics, so the detector chips need to be cooled, typically to liquid nitrogen temperatures (77 Kelvin, about -320.44°F).
From the outer lab, we went through the inner lab and then into the delay line tunnel. To get an interferometer to work, you need the light from each telescope to arrive at the detector at exactly the same time. For light, distance equals time - the further it has to go, the longer it takes to get there - and since no other such 'battery' exists to store light to make it wait for delivery, you build 'delay lines'. These are effectively optical trombones that slide in & out to a particular location, which means the light on that line will arrive at the back end of the system on time.
Such delay lines need to work to a precision ~10 nanometers, so more metrology is used here.
The VLTI is configurable in a variety of ways, as far as which telescopes feed the system on the front end, and which cameras look at the light on the back end, so an optical switchyard helps route the light from the delay lines to the cameras.
The interferometer lab is where the light really gets played with: here the starlight beams from multiple telescopes can be joined together, or "interfered" (hence the name), thereby synthesizing a larger telescope. This is what all the fuss is about: the effective spatial resolution (the amount of detail you can see on the sky) is far greater than one gets with a conventional telescope.
Now, accomplishing this doesn't come for free, so some tools need to be brought to bear on the starlight. Basically, your enemy (well, one of them, besides yourself) is the atmosphere. It conspires to slosh the starlight around such that you cannot properly interfere the light. One of the ways it does that is by changing the delay that each telescope sees, so that the fringes - the product of the interference - move around. One can compensate for that by finding the fringe, and then locking onto it with a tracker before it moves away. Once done, you can follow the fringe around as the atmosphere whacks it back & forth.
However, in addition to an error in delay, the atmosphere also trys to move the light around on the sky - essentially, the familiar twinkling in the stars that we see with our own eyes at night. So, a tip-tilt tracker is also needed to follow the light around.
If one has been successful with all of that, and you get a stabilized fringe out the back end, you can pipe the starlight into a science camera, which dices up the light in a more expansive way to tease out some of the details of the star you're looking at.