-- recording directly to .wav using an emulator
If you have your .sav and .gb on a computer, it may be possible to record your song without the audio leaving the digital realm. Check out Gameboy Emulation and see if there are any programs which have .wav output functionality for your operating system. If not, you can use a Screen Recorder to Record a sound file from your Emulator.
— recording using a microphone
In live situations, your only option may be to use a microphone to record your music. However, microphones color the sound of everything they record. This is true even of expensive/high-end microphones, but don't be scared of coloration, it can add character.
I had been recording using my laptop's built-in microphone and had just assumed that the Gameboy sound chip only used 3 diminishing harmonics. My first recording using the patch cable and adapters revealed 7 harmonics in one instrument. All of them were nearly clipping and at the same volume. That's something to impress the nonbelievers with!
— recording analog signals over patch cables
Another common method of recording tracks is straight out of the 1/8" audio jack on your gameboy. Each model of gameboy sounds slightly different, it may be fun to try all the options out. Just remember: what you have works =)
Depending on the audio-jack-input type of your soundcard, you will have to choose the right cable to to get the analog audio signal safely out of your gameboy's 1/8" jack.
Besides finding the proper cable, you can also string something together using adapters. However, Less connections mean less interference, so the fewer adapters the better.
Audiophiles claim they can hear the difference between regular cables and those with the 24K Gold covering on the tips; Radio Shack makes cables with and without this covering. Interference can be dramatically reduced, for ultra-clean spaces between the sounds.
— direct links to products for recording
Link to the 1/4" to 1/8" adapter:
http://www.radioshack.com/product.asp?catalog%5Fname=CTLG&category%5Fname=&product%5Fid=274%2D875
Link to the 1/8" cable:
Link to 1/4" to 1/8" cable:
http://www.radioshack.com/product.asp?catalog%5Fname=CTLG&category%5Fname=CTLG%5F002%5F001%5F002%5F000&product%5Fid=42%2D2157
*Edit* This is a mono cable. Take a look at the rings on the 1/8" end.
Here is a better cable:
http://www.musiciansfriend.com/srs7/sid=040613150408069141027193699120/g=rec/search/detail/base_pid/333053/
And for those with DJ mixers:
http://www.musiciansfriend.com/srs7/sid=040613150408069141027193699120/g=rec/search/detail/base_pid/333034/