Read the right books and sites to become an Apple ][ master.
A lot of people can have fun with an old Apple ][ or Apple ][ emulator just by putting disks or disk images into the emulator and booting into games. There’s nothing wrong with this, but there’s a lot more that you can do if you like, from looking around old disks to programming in BASIC to crafting new games in 6502 machine language.
Apple produced three versions of DOS which are still in common use. DOS 3.x was the primary version used during the Apple ][ through //e and //c period, supporting only 5.25” floppy disks, with DOS 3.3 becoming the effective standard after its 1980 introduction. ProDOS, which added speed and greater device independence as well as new features like support for directories, first appeared in 1983, and bifurcated into 8-bit and 16-bit versions in 1986. The 16-bit line of ProDOS evolved into OS/GS, a GUI-based environment for the Apple IIgs, which ran from 1987 to its final version, 6.0.1, in 1992. Later versions of OS/GS also had the advantage of being able to read both DOS 3.3 and ProDOS disks, finally breaking a large compatibility barrier.
If you encounter DOS 3.2 disks, also called 13-sector disks, you can use the MUFFIN program on the DOS 3.3 master disk to convert them to 16-sector DOS 3.3 disks.
While DOS 3.3’s master disk includes a FID file utility program, and ProDOS and OS/GS come with applications that let you look around your disks ...