After googling around for a bit, I came across a few basic schematics. This one was the schematic I was planning on following, but I had to deviate slightly.http://web.singnet.com.sg/~lau0cy/pc_midi.gif
My local Fry's Electronics didn't carry a 6N138, but they had the NTE equivalent which I found was a NTE3093. I had resistors at home, but I found I was out of 220 ohm, so I went with 270 ohm, which appear to work just as well.
I didn't care about sending MIDI signals out of my PC, so I left that part out of my design. I wanted all the parts to fit within a DB15 casing.