An Introduction to Emulation
If you've come here not knowing what an emulator, ROM, or the term "modification" in general is, you've found the right place.
What's it all mean?
Cartridges, like the SNES game Chrono Trigger, use "ROM" chips to store data. It's just another way to represent bits by hardwiring their values into a chip. Unlike disk drives though, ROM chips can be accessed like regular memory using the address bus, which is why cartridges don't have loading times.
What most people on the Internet call "ROMs" are just copies of the data made from ROM chips on cartridges and stored in files (usually with some added information in a header that specifies things like the size of the chip and the system type). Technically, you'd call them ROM images, where image in this case means a complete copy of all of the data stored in one medium copied into another medium.
Since part of the data from ROM images for things like SNES games includes the actual code segments (programs) for the games, you can write PC programs that analyze parts of the code and pretend to do what real SNES hardware would do with it (take input, draw to the screen, access data in the ROM). That's all an emulator is, just a program to interpret the machine code for another type of computer.
Since most published games are copyrighted (and will be for another half century or so), it's illegal to download ROM images of games. Most games have a software license on the back or in the manual that also prohibits you from making copies of games you already own.
Technically, the copyright owner of the game could sell ROM images or license others to sell them, but nobody's bothered making a business model out of it, since illegally available ROM images of games are all over the Internet.
In other words, never pay for a ROM image, because it's almost always being illegally copied and sold.
Also, we don't want to advocate copyright infringement here, especially the sort that can hurt Square-Enix's business, so don't use the forums to pass around links to sites that provide illegal copies of copyrighted material like games.
Emulation and Modification
Emulators that can be used with Chrono Trigger can be found at Emulators (Chrono Trigger). While it is illegal to download and have ROMs, it is not to own an emulator.
Since SNES games have been out for a considerably long period of time, several resourceful programmers and curious people have dissected their code and assembly language in order to learn about the games and edit them. This effort was initially confined to simple platformer games, like Super Mario World, but RPGs and other genres were soon examined as well. The culmination of these efforts have mostly been a few spectacular rom hacks (or, modified versions of the games, properly called mods or modifications), and utilities that remove most of the work in editing a game.
Concerning Chrono Trigger, several utilities have been made to edit basic stats, such as those used by Monsters, treasure chests, shops, etc. Most importantly, a rom hacker named Geiger has created an editor called Temporal Flux that allows editing of music instruments, locations, overworlds, dialogue, and event coding (or, the technical script of the game, which directs it and makes it tick). The editor is proposed to become the full vehicle for Chrono Trigger editing sometime in the future.
These utilities have been compiled and organized on the Chrono Compendium's Modification section, should you enjoy editing the game and exploring new possibilities. Good luck, and stay tuned for news regarding Temporal Flux and other hacking.