Basically, you need DOSBox, and that's all. Official version
from the official site usually enough for everyone.
If you are lucky (75-80% of games), using DOSBox is easy.
1. Make link to DOSBOX.EXE at the desktop.
2. Pull main game exe (stars.exe, probably?) over this created dosbox icon.
If you did everything right, it will open DOSBox, mount game dir as C and start .exe in question, essentially running the game for you.
Otherwise, ask here again, preferrably with description what went wrong.
...
Hmm, but all Stars! versions I can found are Win 3.x. In that case it's much worse. You need Win 3.1 DOSBox set. Check it here:
http://www.abandonia.com/vbullet/showthread.php?t=27770. It's not complete though, so you can have some sound problems. Unfortunately, I cannot offer anything better now.