In Minecraft, every nether fortress has a single starting point. It's always a crossing of two bridges. The starting points are predetermined by your map seed. In average, every 768th chunk has a starting point for a nether fortress. These chunks are highlighted in red. The colors of the surrounding chunks are a very rough approximation of the chance to find a piece of a nether fortress in each chunk.
The most reliable way to use this app is to go somewhere inbetween the center and the southeast corner of a chunk with a starting point, and then search for the crossing on different layers. The height level of the crossing is usually between 48 and 70.
The distribution of the starting points is not entirely random (like with slime chunks, for example). The fortresses roughly form a pattern of stripes from north to south. Also, there will always be a minimum distance of 8 chunks between two starting points.
How accurate is it?
The chunks highlighted in the brighter color are merely assumed to contain a piece of a nether fortress. The starting points seem to be 100% accurate though.
Does it work on consoles?
Unfortunately, it does not work on Xbox 360 or PS3. Support for Xbox One and PS4 is currently unknown.
For the reason mentioned above, you need to know the seed of your world to use Nether Fortress Finder, unless, of course, you want to find a seed for a new world. If you're playing SSP, the app is able to fetch the seed from your savegame. Alternatively, you can use the /seed command ingame. In SMP, you can use the same command if you have sufficient rights. Otherwise, however, you're dependent on the server owner, who started the world and has access to the savegame and config files.
Nether Fortress Finder uses some relatively new web technologies. As a result, some features may be disabled for older browsers. So I recommend using the latest version of either Firefox or Google Chrome to avoid any limitations and to get the best performance.
The first thing you should do is select a seed. You can either type it in manually, or you can load it from your savegame. The latter can be done by clicking on "Load from Save..." and selecting your level.dat, or by drag&dropping the level.dat file into your browser window. Level.dat is a small file located in the folder of every Minecraft savegame. You can find the savegames in the saves folder of your Minecraft installation. On Windows you can use %appdata%\.minecraft\saves to get to that folder.
Levels allow you to store and reuse seeds on this website, without having to load your savegame every time. When loading a seed from a level, the seed will automatically be stored as a level.
You should also know that a seed is always a number (up to around 20 digits). If you type in anything else (like letters), it will be converted to a number. Nether Fortress Finder does this the same way Minecraft does, so it's safe to use letters (and other characters) as well.
Once you applied your seed using the "Find Fortresses!" button, you can start using the map. To scroll, use your arrow keys while your mouse cursor points at the map, or move your mouse while holding down down the left mouse button. You can use the slider below the map or your mousewheel for zooming. The lower inputs allow you to go to a specific point (e.g., your base) of the map and set a marker there. You can always remove and add the marker by double clicking on the map. The "Save Map" button allows you to save the currently shown map as png image file.
When using a touch-enabled device, an extra option for enabling/disabling touchscreen control will appear below the map. With that option enabled, you can drag the map with your finger to navigate, you can pinch to zoom in and out, and you can tap and hold to set a marker on the map. By double tapping on the map, you can quickly enable/disable the functionality as well.