So you're interested, you're ready to play, but you don't have the game.
Well you have a couple of options. Go to garage sales, flea markets, thrift shops, or pawn shops and you may find it for as cheap as $1 or less, but it's far more likely to be $2-$8, unless they know what a gem they have on their hands. Then you could be looking at $20+. The game isn't exactly rare, but it can be hard to find since people like to hold onto such a good game. You could also buy it from a used video game store such as Game Crazy. You'd probably pay about $20 there. Unfortunately, many games stores, such as GameStop and EB, have stopped carrying older games. Another option is eBay. Final Fantasy can be found there constantly. Click the video games link, and find your way to NES, games, and then RPGs. Or just do a search on "Final Fantasy", there'll several pages of stuff, probably several copies will be up at any given time. At the time this page was last updated, there were about 50 copies up.
Final Fantasy Origins (where have I heard that name before?) made it very easy to get ahold of FF1. You also get new graphics and FF2 along with the deal. Unfortunately, as a PS1 game, time has passed it by, and it is now out of print. However, it's still out there some places, and used copies are pretty common. Try Amazon, game stores such as GameStop, or eBay.
The Japanese Playstation versions of FF1 & 2 came on separate discs, and the 2-pack comes with mini-figures. Get those on import stores such as Play-Asia, or maybe eBay.
The most recent version is FF1+2: Dawn of Souls for the GameBoy Advance, which should be available in many stores now. It features new dungeons, items, monsters, etc.
Due out some time this year is a new version of FF1 for the PSP. With a higher resolution than any previous version, greatly improved over the other remakes, it's looking pretty nice. It will also feature the new dungeons, monsters, etc. of the GBA version. Expect to find this pretty much everywhere.
Now if you're looking to find the Wonderswan Color version you'll have to find an import shop or try eBay. You can still find the FF1+WSC packages there, and sometimes you can grab one cheap. Just search for "WonderSwan" or maybe "Wonder Swan". Also keep in mind that the WSC version is only available in Japanese.
What about the MSX version? Good luck, that's all I can say. I've seen it for sale on eBay once. Went for a hell of a lot of money though.
Want the cellphone version? Uh... move to Japan, or make friends with somebody there.
But what if you can't buy it? Emulation! An emulator is a program that acts as another computer system. The games are files called "ROMs", which are the actual game code downloaded from the cartridge's ROM chip. You can find a variety of NES emulators at The Emulator Zone and other emulation sites. As for the ROM, you'll have to find that yourself. Doing a search for "nes roms" should eventually end you up on the right track.
You really ought to actually purchase the game if you can though. Emulators can't replace playing it on a real NES on a nice TV, or playing it on the go in the case of the portable version, and of course there is the legal issue, if you are concerned about that sort of thing. (Also, there's currently no NES emulator that can do the game 100% accurately.) I own the game about 9 times over (my original NES cart w/ manual and box, my second copy that's minty fresh and complete, a couple of spares, my FF1&2 Famicom cart, the WSC set, FF Origins, Dawn of Souls, and an extra copy of DoS). Now with all the options available, it is your duty to actually purchase this game!
Final Fantasy Origins at Play-Asia.com
Final Fantasy I & II [pre-owned] at Play-Asia.com
Final Fantasy I & II - Original Soundtrack at Play-Asia.com
All Sounds of Final Fantasy I & II at Play-Asia.com