by using tor browser or an i2p router.
dark web generally refers to .onion addresses in the case of tor. It's cryptographically impossible with current supercomputers as it would need to go through 8 * 10^74 combinations before finding the correct one. to put that into scale, on average, it would take 8 septillion years for a supercomputer to find a value.
Onion addresses can be used for virtually anything, I - for one thing - have implemented a nextcloud instance on tor. That said I have not encountered a onion address that showed anything illegal, but that's also because I haven't been searching.