How did users get NES games onto the NES ROM emulators in the first place? What kind of drive did they use to connect an NES cartridge to a PC?

I've never done this myself, but I'm familiar with the process. Dumping a ROM image requires a reader. In the early days, all game systems used the same EPROM (ROM) chips, and so you could buy a machine that reads or writes to them in order to "dump" an image. These older ROM readers connected to a serial port. Later, as each manufacturer specialized, they began to use different types of chips, so the old readers would not work. Today, each type of console requires a specific kind of reader. Some people build a reader by hacking a NES or other console to get the cartridge interface, controller, and memory bus, and others build one from scratch. I have also seen kits for NES, SNES and GameBoy that accept a cartridge, and plug in via USB. For popular game systems, THIS is probably the way to go, because it even comes with the software. All cartridges for a particular system contain the exact same ROM chip, so that part is consistent (e.g. once you can read one NES cart, you can read them all). Some cartridges contain extra data on separate chips (like Starfox SNES), and you have to dump those chips as well -- which may require even MORE specialized hardware. Once the data is serialized (meaning you can read it one byte at a time), there has to be a hardware interface that reads each byte in order and sends it to the PC. This part has to be purchased or custom made. Then, you have to have software on the PC that reads whatever port you're using (e.g. serial port or USB) and stores the data as a file. Later, some arcade systems, and I think some cartridge-based home systems started encrypting their ROMs as well, so depending on which system, you may also have to hack the hardware to figure out the encryption key -- either it has to be decrypted as it's read, or you have to decrypt the file once saved to the PC. In addition to all of this, some cartridges are compressed (like zip), and so either the emulator or the reader software has to unzip the image as it's read. As I understand it, someone with casual knowledge and skills (such as myself) would not be able to build a reader from scratch, nor use it effectively. Hope this info is educational.