Hey sodaking! It CAN be done! I am listening to an old IBM 600E that has the world's most obscure soundcard, and I know that with time and patience, you will get sound to work on yours too!
First, you need to find out exactly the make/model of your soundcard. This is essential! Without this information, you will have a difficult time getting the drivers configured correctly. Next, if you haven't download/installed the latest version of ALSA, you need to. As you are using Slackware, which I believe comes with ALSA (Advanced Linux Sound Architecture), you can simply go to linuxpackages.net, do a search for alsa, download to a directory on your hard drive (I would use /usr/src/linux. If you don't have that, you can make it easily using mkdir) then cd to that directory and run installpkg to install alsa. Once the install has completed, run alsaconf and follow the prompts. This should do it!
Also, as you are a newbie, you will need to su to root to do the majority of this. If you already knew that, I appologize.
Let me know how it turns out!