How do I colour between lines in vector artwork?
Use Live paint (K) in Vectornation by Zaweba: click a face between lines to fill it, Shift-click an edge to stroke it, with gap detection for open lines.

Use Live paint. In Vectornation by Zaweba, select the line art, choose the Region fill tool (K) and click: the first click makes a live paint group, and after that every click on an area between lines fills that area, like colouring in a book. Shift-click an edge to colour that stretch of line, and Alt-click a face to clear its fill.
In ordinary vector drawing, a fill belongs to a whole closed shape. That is awkward with line art, where the areas you want to colour are made by several lines crossing each other and are not shapes in their own right. Live paint treats every enclosed region as something you can fill, whatever lines made it.
Filling faces and edges
Draw or open your line art. It can be pencil lines, pen paths or traced artwork. Select all of it.
Pick Region fill (K) and click on the selection. That first click turns it into a live paint group. Choose a fill colour, then click on any face, that is, any area bounded by lines, to fill it. Alt-click to set a face to no fill.
Shift-click an edge to stroke it. In a live paint group, an edge is the part of a line between two crossings, so you can colour one stretch of a line differently from the rest or hide it altogether.
Use the Region picker (Shift+L) when you want to select faces or edges rather than paint them, for example to change several at once.
Gaps and editing
Hand-drawn lines rarely meet exactly. Live paint has gap detection, which treats small gaps as closed so the colour stays inside rather than flooding the neighbouring area. If colour leaks through, look for a gap that is larger than the setting allows and either close it or adjust the gap detection.
Live paint follows edits to its paths. Move a line or reshape a curve and the fills adjust to the new regions. You can also Merge more paths into the group.
Finishing up
Under Object > Live paint you will find Make, Expand and Release. Make creates a group from a selection. Expand turns the live paint group into ordinary shapes, one per filled area, which is useful when you need plain vector shapes to send elsewhere. Release turns it back into the original paths without the colour.
Keep a live copy before you expand, so you can come back and recolour later.
Colouring line art well
Draw the lines first and colour last. Live paint works best on finished line work, and the colouring goes very quickly once the lines are right.
Use global swatches for the main colours, so if the client asks for a different blue you change one swatch rather than refilling every area.
If you started from a picture, Vectornation's image trace can turn line art into paths first, or trace it as centre lines, which then make a good base for Live paint.
Shape builder instead
For a design built from overlapping shapes rather than lines, the shape builder can merge and split areas into new shapes. Live paint is the better choice for drawn line art, and the shape builder for geometric construction.
Vectornation by Zaweba is free software for Windows that works offline and needs no account.