When you say exporting the palette do you mean from your image editor so you can stick it back into the game or originally from the game itself?
It sounds like the latter and in that case I have to ask whether you intend to change the colours or just use existing ones and tweak the image. Either way it is a fairly fundamental part of graphics hacking. The tutorial actually tells you what you need to do (the palettes are stored in plaintext at 690 hex after the start of the portrait in question) but I will cover basic palette extraction anyway.
The SNES is not like some older systems and can have a selection of colours that make up a given colour palette (you can even change them during runtime as a type of animation). It does this by having the developer choose a selection of colours (they are anything in the 15 bit range for 555 BGR which is also the same as the GBA and DS in case you find other tools aimed more at them, or some 32768 colours) but you can only have 256 of those loaded at once*. Actually I say 256 but there is http://en.wikibooks.org/wiki/Super_NES_Programming/Graphics_tutorial#Bit_Depths
to consider which basically says there are real and virtual modes that it can be carved into and oddities beyond that so you may end up a bit more restricted (though it does not look to be the case here).
*it looks like you are not having it happen here but there are blending options which up this number a bit further.
By necessity the game will have to have this loaded into memory so if you get to the point in the game where the image is displayed then you can probably export it directly from the emulator and various tile editors will be able to pull them from savestates (and from there you can export it to more general formats for more exotic image editors).
If you just want to mod using existing colours this works well. You will have to enforce tile editing discipline and thus you will not be as able to do things like gradients, noise functions, colour blending, anti aliasing and everything else that works but changing/blending colours according to a mathematical function. This is not as bad as it might seem as you can still be sharply limited when you have though importing "real" images can be tricky.
If you want to change what colours you have available then you get to find the palette within the ROM. The obvious start is to search for the relevant fragment in the ROM -- palettes are small and thus not often compressed so they can be sitting there plain as day in the ROM.
Alternatively with the virtual modes, animation (you can change colours, maybe do a bit of contrast adjustment and more*), simple palette construction and more the above might not work and you will have to trace it like you when finding another image.
*I have not hacked a wide enough selection of SNES ROMs to call it but the GBA, which is basically SNES junior/little SNES, it is quite common and on the DS, which is basically SNES junior plus, then it is very common indeed.
If those pictures are used as an animation (losing face, injured face....) then it might be a different palette for every one (SNES coders were usually a bit tighter than that but I am not going to put money on it not happening) and it may also be a different palette for every