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I recently saw the first image of a black hole. As I understood, it is covered with bright, hot matter. In this case, how can we see the black disk (event horizon), instead of a bright disk due to the matter surrounding the black hole? Or is the matter around the black hole disposed in a disk shape and the astronomers got lucky that the disk was not oriented towards Earth?

What's going on here is that you have been misled into thinking the ring-like structure has anything to do with the accretion disk. It doesn't, or at least only indirectly.

The disk is referred to as geometrically thick, but optically thin (see sections 1 and 2 of paper V issued by the Event Horizon Telescope collaboration on 10 April 2019). This is actually the opposite of the disk visualised in the film "Interstellar".

Because the disk is geometrically thick, it covers the whole picture. Because it is optically thin, we can see through it to the black hole. That is the basic answer to your question.

In an optically thin plasma, the brightness you will see is proportional to the optical path length (physical length multiplied by an absorption coefficient) along that sightline. The photon ring marks radiation travelling towards us that has been bent around the black hole, or has even orbited it several times. Hence those sight lines have larger optical path lengths and that is why we see it as a bright ring.

Radiation travelling towards us from plasma in front of the black hole, has a small optical path length and is not very bright. In addition, the sight lines to plasma behind the black hole cannot travel through the black hole or even close to the event horizon. Hence the circular "shadow" inside the photon ring.

The black hole image that you saw is not a photograph in the traditional sense. A traditional photograph is created when visible light strikes a digital sensor or film in a camera.

The image of M87 that you saw was created by an elaborate, complex, globe-spanning and labor-intensive operation.

To start with, the telescopes used were radio telescopes. These radio telescopes "see" radio waves with a 1.3mm wavelength like we see visible light, which has a wavelength from violet (380 nanometers) to red (700 nanometers). Think of it like infrared vision or night vision.

Eight radio telescopes all over the globe were pointed toward the same black hole at the same time over the course of four days. Each radio telescope collected an enormous amount of data by observing the black hole in the radio spectrum, not the visible light spectrum. According to the Event Horizons Telescope website, each of the eight radio telescopes produced about 350 terabytes of data per day. This radio spectrum observation data was timestamped using an extremely accurate atomic clock at each location.

The data was then shipped to supercomputing centers to be processed by an algorithm. The computer algorithms work by lining up the data from the different telescopes using the accurate timestamps and by aligning the observed data spatially. This process is called very-long-baseline interferometry (VLBI). The basic idea is that if you take two distinct observations of the same object from different locations and synchronize them. This helps to eliminate atmospheric noise by seeing what both different images have in common. While it may seem like a highly artificial process, it is very effective at eliminating noise.

The image you see is therefore the result of a computer algorithm processing radio observations of the black hole from 8 different locations on earth. The choice of color was likely a choice made by the computer scientists who wrote the algorithm, but it appears to bear some relation to the intensity of the radio energies observed: more energy shows as brighter, while darker spots with less energy are deeper red or black. This choice of color might make sense because the strong gravity of a black hole will tend to redshift any light emanating from nearby or passing close to the black hole. On the other hand, black holes are said to be enormously energetic in a broad spectrum of electromagnetic energy. First-hand accounts of nuclear explosions, which unleash X Rays and Gamma Rays and other far-ultraviolet energy have been described as having all kinds of exotic color.

While this may seem a bit disappointing, it's worth noting that visible light does not propagate through space as well as radio. Radio penetrates dust and gas and all the intervening detritus in space much better. Visible light tends to be blocked and re-absorbed. Think of Wifi signals (radio) versus visible light. The Wifi penetrates walls, while the visible light gets blocked by walls, curtains, etc. The EHT website has some helpful infographics on VLBI.

The black part in the centre of the image genuinely represents some directions from which less energy is arriving at the telescopes. I believe the intensity in the middle of it is about 10 times lower than the intensity in the bright ring around it. So in that sense it really is a dark spot.

It is described in the papers as the "shadow" of the black hole, although even that is stretching the word shadow a little. Basically the light that "would have" been coming to us from that direction has been bent away by gravity.