1. BACK UP YOUR DIRECTORY OF EXTRACTED FILES.
2. Decide exactly what you want to edit. The basic MvC2 colors are documented here. You will have to painstakingly edit each character per button-selection type, so start with just one.
3. Open PalMod.exe. Go to the File menu. Browse to your directory of extracted files. At this point you should see this:
4. The first drop-down listbox lets you select which character to edit. Set that to the character you want to edit.
5. Click Preview
6. Use the second drop-down listbox to select which color you want to edit.
7. For each of the 16 color boxes:
   1. Click it.
   2. Click the Blink (Sel) button. Now you know what it affects.
8. Adjust colors!!! Press SET to see it in action. You can Undo (CTRL-Z) or Redo (CTRL-Y) changes. If you want to figure out what the codes are for any given color, you can always view a different character who has the colors you want.
9. When you're done, save your changes with APPLY or just discard them by switching to any other palette.
10. So now you've edited one character's single palette. One stupid problem is that multiple palettes are used per character button-type (say, LP). Verify that you've edited that character corrrectly according to Eidrian's palette guide. If there are multiple palettes that need to be edited, it'll be listed there. If you don't edit those, the character won't look right.
11. Now copy those files to your Extracted Data directory, then follow the Create ISO and Burn CD steps and you're good to go. =D

People who use multiple palettes
Many characters are hard to edit because different palettes are used for different character sprites/poses. They must be edited carefully or they'll look buggy. If they do use multiple palettes, Eidrian's guide covers how to edit them correctly:

Examples/What it looks like

Color/sprite references:

Character color references to copy (no work!)