Okay, the basic idea:
PS1 game doesn't work is any PS system available to you
It reads in your PC fine, or near fine
You want to be able to play these off of your computer

That's it! Everything is free! (except the game, obviously)

Oh, by the way, this is my first instructable, so don't hate me too much for this. D:

Step 1: Reason

Maybe you want to have it on your awesomesauce monitor, or maybe your PS1 self ignited on your carpet, who cares!

I guess I'll go ahead and tell you mine.
I loved my PS1 copy of Marvel Vs. Capcom, like a child. Sadly, my PS2 had different plans. So did my PS3. I wanted my baby back, so I got mad.

After doing it the first time, I decided to revive my Twisted Metal 2 disc as well. :D

Step 2: Required Software, Etc.

Okay, we need a couple tools.

Software:
A PS1 Emulator of your choice (I recommend ePSXe)
ISO file burner (I used ImgBurn)

Both of these are free, and can easily be found through google.

Hardware:
PS1 Disc - It doesn't have to be perfect, but it can't be too horrible
Computer that works (Semi at least :P)
Disc Drive that can read an old crap disc

Well, that's it, once you get all of this installed, proceed to the next step after reading the very large and scary disclaimer at the bottom.

I'm in no way or form responsible for any damage, or anything else related to these instructions you a reading. Don't blame me if you screw up.

Step 3: Creating an ISO Using Your PSX Disc

Alright, time to do some work! Pop your disc in and wait for it to do whatever it tries to do. Cancel whatever your computer tries to do and open up ImgBurn. Let it load up and then click the button that says "Create image file from disc" Don't mess with any options other then the destination for the file and then click the go button. (It's the bottom right corner one that's big and has a Disc with an arrow pointing to a file with a disc on it)

Don't worry if it takes a while, it's okay, if any errors come up, don't worry, sometimes it doesn't matter, just bypass them. Once you hear this weird success noise, click on the next step!

Also, once it's done, your can take out your disc, and destroy it for all I care. (READ THE DISCLAIMER BEFORE YOU YELL AT ME FOR SAYING THAT)

Step 4: Open Your PSX Emu and Play!

Open up your PSX emulator, in my case, ePSXe, and look for something like "Open ISO" or "Open IMG", or any other kind of open type thing. Browse, look for the file you made from your disc, and click open. Now like, oh mah gawd, ps1 goodness.

Have fun!