For starters what game?
not sure what kind of program you expect, the process is the same for any game if you don't have an editor built for the game, just recording video and/or taking screenshots.
You could try Dragon Unpacker, if your lucky it can extract them from the game files.
http://en.www.elberethzone.net/dragon-unpacker.html
It can't hurt to search info about the old game and the file extensions it's using. You might be able to dig up some legacy software that can directly edit/export images from that particular game, or the common asset files that were used by that game company. Sadly you wont find many games like this thou, but there are some commonly used formats from that era that can be edited using old tools.
Or if you can run it under windows95 you could run it under dosbox and record video.
you can use PCXCLEAN made by elecbyte to speed to automate cleaning screenshots. You create a palette file with all the colours your sprite needs. The program removes all the colours that are not in your palette and replaces them with transparent/pink/whatever. You'll still have to clean some junk out thou probably. The program is a an old DOS app thou, it might even need dosbox to run, I can't remember OTOH.
You can also use a memory editor like ArtMoney to rip sprites from memory, but it's complicated and tedious.
http://www.artmoney.ru/