Can anyone tell me how to connect my studio monitor speakers with an XLR or 1/4 inch TRS input to my 1/8 inch stereo output on my computer sound card? I don't see any adapters or cords that convert TRS to regular unbalanced stereo. Is this is possible without a mixer?
You can get adapters for this, but the sound will be much better if you get a sound card that has the TRS outputs, or if you use an external breakout box (USB or Firewire, USB on most PCs.)
The problem with an adapter is that you lose the features balanced outputs gives you - most importantly is the low noise floor and immunity to interference balanced cables give you.
As Neil says, get a decent sound card with balanced outputs.