How do I find out the mythology and history of my Fortress?

For an immersive approach, have your dwarves create art. This can include statues, engravings on walls or floors, and decorations on other objects.

These works of art will often depict significant historical or mythological figures relevant to your fortress or the artist dwarf. However, such pieces of art will not include a description of what they're referencing, leaving that for you to figure out.

The easiest way to do this is to make a copy of your save, load up the fortress in the copy, then abandon the fortress and start up the game again in Legends mode.

If you're running dfhack, one approach is to use the command exportlegends all to generate a set of files with the world information, and then access those files with an external tool like Legends Viewer (Windows) or Legends Browser (cross-platform). One advantage of this is that it does not require abandoning your fortress or moving save files around.

Similar xml files can also be created from Legends Mode without use of dfhack.

This has the drawback of being more complicated, but many people find that these tools have nicer interfaces than Legends Mode itself.