I just had the outlines as top layer as they only have the outlines anyways while the rest is transparent. If the outline layer is not transparent but filled with white, just change the mode to "Multiply" instead of "Normal" to have the colours below shining through the non-black areas.

Below the outlines there are the different colour layers. It's easier to get a result by diverting the colours onto many single layers, like one for the hair, one for the eyebrows, one for the face, one for the neck and so on. These layers contain the base colour only, no shadows or highlights or whatsoever.
It is important to select the right area precisely to make the colours fit very well. The usual approach is as following: Use Magic Wand tool with Tolerance somewhere between 10 and 100 and select the general area for a certain colour, let's say the hair for example. If the to be coloured area is diverted by the outlines into several paths, just add each part with shift-click using the magic wand. When everything which is supposed to have a certain colour is selected, go "Select -> Modify -> Expand" and expand the selection by one or two pixels (depending on the width of your outlines. Usually expending by one pixel is best). Now some parts might not have been selected properly, especially in sharp edges. Just add these parts with the Lasso tool to your selection.
Then fill the colour into the colour layer (name each of them properly as with this method a lot of layers will be created). If there still are white spots where no are supposed to be, just paint them with the Brush tool.


For each colour layer, I create one layer mask with standard settings (normal/100% and so on). I put the shadows and possible highlights on these. It is easier to make them fit this way then putting them directly on the layer below, as the pixels on the layer mask will only be displayed if there's something on the layer undeath it: Means, if you for example paint black shadows onto the hair, these brush strokes will only be visible where there is hair underneath it.
I usually paint hard shadows (like every single of those used for hinata as I did not do any soft shading) with the Pen tool and use "Fill Path". For Soft Shading and Highlights I use the Gradient Tool (Settings "From Foreground to Transparent", Opacity 5-20%, Linear Gradient/Radial Gradient/Reflected Gradient). For the highlight on Hinata's Konoha badge I used a Linear Gradient from the top and a Reflected Gradient in the middle for example.

For highlights in the eye, it might be best to create a layer on top of the outlines layer and paint the highlight with the brush tool at a very low "Hardness" setting for the brush (you can select this where the brush size is selected, too). This way it will shine above the pupil outlines and look much better.

For the background I just used the original file and filled some areas with Fill or gradients using the "Multiply" mode to maintain the outlines.

Thorfinn lays in ambush:


And: Fi in a space suit (from "Planetes"):


And: The Jarl and the Thrall from Vinland Saga: