Using the Shape Builder in Paint by Zaweba
The Shape Builder in Paint by Zaweba merges overlapping shape pieces with a click or drag, and Alt removes them, so you can sculpt shapes by hand.

Boolean commands are precise, but they make you think in terms of top and bottom, cutter and target. The Shape Builder lets you skip that. You lay down overlapping shapes, look at the pieces their edges create, and then simply click or drag across the pieces you want to keep together. In Paint by Zaweba it sits in the toolbox on the U key.
Hold Alt and the same gesture deletes pieces instead. Between those two moves you can carve out most simple shapes without opening a menu.
How it thinks about your shapes
When shapes overlap, their outlines cut the area into regions. Two overlapping circles make three regions: the left crescent, the lens in the middle and the right crescent. The Shape Builder treats each region as a piece you can pick. Drag from the left crescent through the lens and those two merge into one shape, leaving the right crescent on its own. Alt-click the lens and it vanishes, leaving two crescents that no longer touch.
That makes it a fast way to reach shapes that would take two or three boolean steps. A moon, a cloud with a flat base, a heart built from two circles and a rotated square, a keyhole from a circle and a trapezium: all of these come from overlapping a few basic shapes and then working the pieces.
A good way to work
Start with simple, generous shapes and let them overlap freely. It is easier to throw away regions than to add material later. Zoom in enough that small slivers are easy to hit, since a sliver missed at the edge of a drag stays as a separate piece.
Drag in a single sweep when you want several pieces to become one. A stop-start sequence of clicks also works, but a single drag shows your intention clearly and leaves fewer stray bits. Then switch to Alt and tidy up the leftovers. If something goes wrong, undo and sweep again; it is quicker than trying to repair a half-merged result.
Once the outline looks right, it is still an ordinary shape layer. You can fill it with a gradient, give it a stroke, round its corners with the Corner tool or line it up with the Align commands. Many people find it helps to finish with Merge Shape Components from the Vector menu so the final path is one clean outline.
When to use the Shape Builder and when to use booleans
The Shape Builder suits shapes you are designing by eye, where you are deciding as you go which parts belong. Unite, Subtract Front, Intersect and Exclude Overlapping Shapes in the Vector menu suit repeatable steps where you already know the operation, such as cutting the same hole into a set of icons. Both work on the same kind of shape layer, so you can mix them freely in one design.
Common snags
If clicking does nothing, check that the layers you are working on are shape layers rather than pixels. A shape that has been rasterised has no regions left to pick. You can redraw it, or use Vectorise Bitmap to trace it back into shapes first.
If a drag merges more than you meant, it probably clipped the corner of a neighbouring region on the way past. Undo, zoom in and take a straighter path. And if the result has a faint seam where two pieces joined, merge the components so the outline is rebuilt as one path.
Where the Shape Builder fits
Paint by Zaweba is mainly an image editor, so the Shape Builder is there for the moments when a photo or a poster needs a clean graphic element: a sticker shape for a label, a frame for a headshot, a simple icon for a thumbnail. It saves a trip to a separate drawing program, and because the result stays vector, you can scale it up for print later without it going soft.