I found my original copy. Is there a way to install it using 64bit windows 7? Like an easy way? I've done some research and it looks like it might be possible but seems complicated.

Or should I just buy it from GOG? I'd rather save the $10 since I found my original cd from long ago

Once you've gotten into DOSBox, installing and playing TIE Fighter shouldn't be a problem, even on Win 7 x64. :)
http://www.dosbox.com/

FekLeyrTarg is correct, you just need to install and use DOSBox in order to install and run the game. DOSBox can be a little tricky to figure out but if you've played the oroginal game on DOS you shouldn't have any problems getting set up. Just follow the instructions on the DOSBox website and wiki page.

The super-short version is that you "mount" a folder on your computer that will pretend to be the C:\ drive in DOSBox. Then you can run DOSBox and use DOS commands normally, including running the TIE Fighte installer and the game.

You should also note that it's a good idea to tweak the DOSBox configuratoin file for the game. There's a great guide for a few important changes for X-Wing, but you should make similar changes for TIE Fighter:

http://www.gog.com/forum/star_wars_xwing_and_tie_fighter_series/xwing_1994_tweak_guide_video_graphics_sound_music_speed_and_controls/page1

Also note that there's a weird timing bug with both X-Wing and TIE Fighter that causes turrets to not shoot at you when the game is running fast. Slowing down the game fixes this but introduces lag and stutter. You have to find a compromise. There are a bunch of threads around here about this issue, including this one:

http://www.gog.com/forum/star_wars_tie_fighter_special_edition/tie_fighter_collectors_cd_dos_a_serious_bug/page1