Here are some of the most common causes of the non-manifold error and how to fix them. Below you'll find a written description, but if you prefer a visual aid, you can check this video for help.
1. Merging intersecting volumes: When combining 2 or more intersecting volumes, you must use the Stitch and Scoop (Boolean) tools to resolve the intersections. You can merge or group non-intersecting objects without any problems, but if they intersect, you need to use the Boolean tool, or you will get a non-manifold geometry. This also means you need to ungroup all intersecting objects before using Union.
2. Flipped normals: Stitch and Scoop will wrongly calculate the object's volume when one or more intersecting objects have flipped normals. You can turn on the Backface Coloring display to see if an object has flipped normals and then use the Flip Normals tool to correct them as needed.
3. Touching instead of interesting: Stitch and Scoop can create wrong outputs when working with objects that only touch and do not intersect. The solution is to scale one of the objects, even by just a fraction to make them intersect, use Stitch and Scoop, and then scale it down if needed. Using different colors for each volume can be helpful, so you can later use the material selection to select and scale back that part.
4. Connecting edges without volume: The entire object must have a connected volume, and edge-only connections are considered non-manifold. Edit Details tools are great for manually fixing problematic intersections (if you can find the problem), while MagicFix can automatically fix the entire object. It's not perfect and will not yield the same nice output, but it's a quick and easy fix for most such issues.
5. Missing faces: Every object must be completely closed to calculate its volume; if you have missing faces, you can use the Fill polygon tool to close them. If you are also missing edges, you can use the Edit Details tools to add the missing edges and thereby close the volume.
6. Self-intersecting faces: Backface Coloring can help find self-intersections. In some cases, you can manually correct them; others may need MagicFix to rebuild them.
7. Duplicated vertices: The volume on an object must be watertight, which means that each connecting edge must share the same vertex with all other connecting edges so that you can’t move one vertex without simultaneously moving the other connecting edges. You can use the Geometry Clean remove Duplicate tool, to solve such problems.