I would've made a "MUGEN Database:Palette Galleries" page, but I wanted you lot to comment on it if you don't understand or whatever :)
NEW AWESOME METHOD
I'd advise you use this over the old one!
Get yourself a copy of Fighter Factory 3. What's good about FF3 is it can read .sffv2 sprite files and export images...with transparency!
Make sure the image shown is the first sprite (0, 0), which should be the first frame of the character's idle animation. Then all you've got to do is hit the save button , save it as something like CREATORCHARACTERpalx.png, with "x" being the palette number (don't be a pillock and literally call it CREATORCHARACTERpalx.png - an example would be GMGarchomppal1.png, or FreezaZ2pal6.png), move the second slider (the one below the image) across one, and repeat. Also, pay attention to the numbers next to the slider; the palettes are typically 1,1 - 1,12, so if you're at 9000,1, then you've gone too far :P
OLD OUTDATED METHOD
I'm using FFU (Fighter Factory Ultimate) for this, so if you have anything other than FFU, let me know and I'll figure it out :P
You open FFU and open up your desired character; I'll be using Rotom.
Once on the Palettes tab, you should see something similar to this (as well as all of the buttons, etc. which are not used in this tutorial):
Take a Printscreen (PrtScr) and paste it into an image editing program like Photoshop (if you don't have that, use Gimp, because it's free). DON'T USE PAINT, AS IT DOESN'T HAVE TRANSPARENCY!!!
Use the Magic Wand tool (or whatever allows you to make the background transparent) and save it as a .png, but call it whatever you want (best to name it something related to the character, and not just Spanglyweff.png, unless the character is called Spanglyweff; I generally name the palettes "Nameofcharacterpalx", with "x" being the palette number).
The end result
Your result should be something like this:
Think you're done? Nope (unless the character only has one palette). You have to repeat the above process with all the palettes!
Once you've tired yourself out with all this work, you use Special:MultipleUpload to upload all of your wonderful palettes! Add your palettes into your desired character article under the Palette Gallery section in the order of 1-12.
Publish the article.