Please explain with screenshots how to do this and how and in which order and where I have to place and activate the quarry and the landmarks. I have read that this is possible, but I fail at replicating this.
The Buildcraft quarry doesn't support areas larger than 64x64. Quarry+ adds a block called Quarry+ which can support up to 256x256.
If you have Extra-utilities installed then use the Ender Quarry, it can support an unlimited* (read stupidly large) area.
It is not possible to build a quarry larger than 64x64, which is stated on the wiki:
I would recommend placing a number of quarries adjacent to each other and connecting them together with pipes.
Guess what? You CAN use the quarry for greater than 64x64 areas! It's not a limitation of the quarry, but rather that it's difficult to get landmarks to form an area like that, as they can only connect to other landmarks up to a certain distance away (63 or 64, depending on how you count it, I think). (I will grant that perhaps it has become possible in the time since the other answers were posted, but evidence faintly suggests otherwise.) After a great deal of experimentation and looking at source code, I've figured out how to get, for instance, a ~192x192 landmarked area, which the quarry can use.
Note, before we begin, that as mentioned on http://feed-the-beast.wikia.com/wiki/Quarry, which I think you've read, the quarry is limited by forgeChunkLoading.cfg's
Note also that I'm using Minecraft 1.7.10, with the relevant Forge 10.13.4.1517, and BuildCraft 7.1.9.
Here's the basic process. I'm doing it here with the landmarks having only a single space between them, but it also worked (for me, several times) with the landmarks at max distance. Just scale it up as desired. Remember to place redstone torches next to your landmarks to see what the max distance is to their next neighbor.
Also, it MAY matter which orientation you do this in - N/E/S/W; I recommend doing it the orientation I've written, if possible.
Here's some pictures of it on the 192x192 scale, on a flatland I made in MCEdit. Each checker-tile is a chunk, and I've colored each 4x4 square of chunks in alternating colors to mark approx how big a quarry can usually be. Here it is starting to mine: Here's the quarry (in a different spot; different test run), text saying it'll keep 145 chunks loaded: (Still 3x3 max-areas, btw.) After increasing my maximumChunksPerTicket, I set up a 6x7 max-area quarry, which loaded 672 chunks. (Got one of the dimensions wrong, somehow, or it'd be a 7x7.) At that scale, it was visually a little glitchy, like lasers disappearing as you reached the farther landmarks, or the digging-arm being invisible. I suspect it's something to do with a maximum visual length of such objects, or possibly something to do with chunk-loading, though that makes less sense once the quarry's in place. Either way, it works fine. I did run around the perimeter once before placing the quarry, to make sure the chunks loaded once more before I put down the quarry. Dunno if that's necessary.
That should do it! Hereafter follows a brief explanation of why I think it exhibits this behavior.
This is all related to how landmarks keep track of the area they mark: they each store a variable for the dimensions of the box that encompasses them. They try to keep it in sync with the other landmarks in the structure, but I'm not convinced it's quite right - I think that's part of why you end up with odd sub-areas. As you add landmarks to the edges of the structure, it inherits the origin and dimensions of the box, expanding the box to include its(landmark)self.
Side note, each landmark has 3 variables, one each for their neighbors on the X, Y, and Z axis, respectively. When checking for neighbors (when you right-click on it) it checks in the following order: +x -x +y -y +z -z. Honestly, though, the behavior of the landmarks still looks a little erratic to me, and not fully in line with what I expected, given the code.