There are many ways to do this; here's a walkthrough using Gimp.
1. Resize your source imageI see from your other thread that you just scaled the image to 120x140. If you don't want the image to get squashed I suggest cropping it first (Image -> Canvas Size).
First, click the 'link' icon to prevent the aspect ratio from being preserved when you alter the width. The ratio of height to width is 1.1666... for the large portrait, so I've changed the width from 520 to 464/1.1666... = 398. Then in the Offset preview I've dragged the image so that the face is centred in the new canvas.
Click Resize to crop the image, then from the Layer menu select Layer to Image size.
2. Adjust colours (optional)When your source image is a jpeg off the internet (as in this case) you might want to tweak it a bit to improve the way it looks in Mugen. I suggest upping the contrast a bit:
3. Remove background (optional)There are several tools to help with this. The most useful is the magic wand (selects areas of similar colours - experiment with the Threshold setting). The idea is to select just the portrait and erase the rest. The steps I use:
(a) select the background areas (hold down shift and click the background areas with the magic wand to build up the selection - use undo if you accidentally select part of the portrait);
(b) open the Select menu and click Invert - you should now have just the portrait selected;
(c) Copy then Paste, then open the Layer menu and select New Layer;
(d) Open the Layers dialog (Windows -> Dockable Dialogs -> Layers). You should have two layers:
Select the bottom layer and click the trashcan icon to delete it. You should be left with just the portrait, with no background:
4. Scale the imageHere's where you resize the portrait to the required dimensions. From the Image menu select Scale Image and change the width to 120 pixels. The height should automatically be changed to 140 if the "preserve aspect ratio" option is active.
If you removed the backgroud (step 3) you should now fill the space with a colour that isn't used anywhere in the image. Usually I'd use bright pink or green for this but in this example there are a few pinks, purples and greens in use, so maybe try red. At this point you might need to do a bit of cleanup on the background as there might be a few stray pixels that were previously missed. Try to ensure you have a black outline, with no light grays or other colours around the edges.
5. Index (create a palette)We need to reduce the number of colours in the image to 255. Open the Image menu and select Mode -> Indexed. Select "Generate optimum palette" with 255 colours and click Convert. This will result in an indexed image but our background colour probably won't have an index of 0, which is required by Mugen. To correct this, open the Colours menu and select Map -> Rearrange Colourmap. Find the colour you used for the background and drag it to position 0, then click OK.
6. SaveThe image should now be ready. Save as a PCX (if you click Save As and enter a name of Portrait.pcx then Gimp should automatically save it in PCX format). If you're prompted about layers or transparency just choose the default options.
You should now be able to insert the portrait using Fighter Factory and if you did everything correctly, all should be well.