How to merge overlapping shapes into one
Merge overlapping shapes in Vectornation by Zaweba with the Pathfinder panel or by dragging across them with the Shape builder tool.

Two tools in Vectornation by Zaweba merge overlapping shapes into one. The Pathfinder panel combines a selection in a single click, and the Shape builder tool lets you drag across the regions you want joined, so you choose exactly which parts become one. Both give you a single clean shape in place of a stack of overlapping ones.
Merging is one of the everyday jobs in vector drawing. Logos, icons and illustrations are often easiest to build from simple circles and rectangles, and then join into one outline. A single shape is lighter, easier to colour, and cuts cleanly on a vinyl or laser cutter, which would otherwise follow every overlapping edge.
Using the Pathfinder panel
Select the shapes you want to combine and open the Pathfinder panel. It holds all ten Pathfinder operations, including the one that joins shapes together into a single outline, along with operations that subtract one shape from another, keep only the overlap and divide shapes along their edges. Pick the join and the selected shapes become one.
The panel can also make live compound shapes. A live compound keeps the original pieces inside, so you can still move a circle or resize a rectangle and the merged outline updates. That is the better choice while a design is still changing. When it is settled, expand it to a plain path.
The same operations are available as live effects too, so you can apply a merge through the Appearance panel and keep it adjustable alongside other effects.
Using the Shape builder
The Shape builder is more hands on. Select the overlapping shapes, choose the tool, and drag across the regions you want merged. Every area your drag passes through becomes part of one shape. It works on the pieces made by the overlaps, so you can join some regions and leave others alone, which Pathfinder can't do in one step.
The Shape builder also deletes. Use it to remove a region, such as the middle of a ring or an unwanted overlap, as you go. Combine and delete in one tool and you can carve a complicated shape out of simple parts very quickly.
Since version 0.9.0 the Shape builder has gap detection, which helps when shapes almost touch rather than overlap. Small gaps can be treated as closed, so the region between them can be filled and merged.
Which one to choose
Pathfinder is the quick option for straightforward merges, especially of many shapes at once, and the only one that offers live compounds. The Shape builder is better when you want to pick and choose regions, or when the shape you want is made of parts of several shapes rather than all of them.
Many people use both. Rough out a design with Pathfinder, then refine it with the Shape builder.
Avoiding a messy result
Shapes need to overlap or meet properly. Two circles that look as though they touch but sit a hair apart will stay separate when you merge them, leaving a gap. Zoom in to check, or use the Shape builder with gap detection.
Fill and stroke come from one of the shapes, usually the top or front one. If the merged shape takes on a colour you didn't expect, just set the fill again.
After a merge, run a quick tidy. Object > Path has clean up, simplify and remove anchor point commands that take away any stray points where the old shapes met.
Building complex outlines from simple pieces is how most good logos and icons are made. Vectornation by Zaweba gives you both the quick route and the precise one.