Basically: Use debug mode, turn off the hud, stages, etc., so all you can see is the characters on a black background.
Find a good pose. Note the frame of the animation the character is in when they're doing it. And also use a location that you can consistently get the character into exactly, such as where they spawn or the edge of something. Use the freeze game feature so you don't have the pause screen in your screenshot, and so you can advance frames until you get to the right frame of animation
There are a couple different ways to get the camera to go into the exact same place every time. One is to use Dolphin's "Free Look" function, found in Graphics Config -> Advanced. The way that works is you can use keyboard controls to step the camera in different directions. You can also adjust how much the camera moves from each step. You can use this to get the camera to the position you want by counting how many steps you take in each direction of movement, until you get it into the correct place.
The method I came up with, which I prefer, is to set the RAM addresses for the camera's position & direction via hotkeyed scripts (one for saving positions, another for loading) while the game is playing in Debug Dolphin. That gets more complicated though. Another way you can do this is with a simple Gecko code, or by manually changing the RAM while the game is running.
Here are the addresses you need to go to to get/set all facets of the camera:
80452c6c
80453040
80453044
80453048
8045304c
80453050
80453054
80453058
You can just use a bunch of 04 codes to make a Gecko code to set your position once you have the values you need.
Important note is that this only works when the camera is in 'Free Roam' mode, by which I mean the debug mode camera where you can pan as well as zoom/rotate. The camera mode the game is in is stored in RAM here: 80452C6C It basically acts as a mode switch too, since I believe you can change that and the game will update.
After you have all your screenshots, take them into an image editor, crop them to 136x188, remove the black from around the characters, add a shadow, add a palette, and save the image as a png. Like I said, I have scripts for all the editing which I'll try to upload soon.