I recommend doing this in a new, empty Sketchup file, so that you can clean up the tags and avoid making your working files messy.
File > Import > DWG. The CAD file will be imported as a SketchUp component, and its file name will automatically become the component name.
View > Hidden objects and Hidden geometry.
Delete any irrelevant objects outside the plan.
Under Tags, look for tag/layers that are turned off (hidden). If you don't need these hidden layers, select those tags > delete > delete entities.
Under Tags, select all tags > assign to Untagged. CAD layer colours will be preserved as SketchUp materials, so you can still select according to layer by selecting according to material with Selection Toys.
Export > DWG
When exporting plans, sections, or elevations, make sure you're using a preset orthogonal view, or that the view is parallel to a surface.
Rhino 7: Export directly to Sketchup 2021
Rhino 6: Export to Sketchup 2019
Export DWG
Export FBX
Rhino 7: Export directly to Sketchup 2021
Rhino 6: Export to Sketchup 2019
Export OBJ with preset: Rhino
Rhino 7: Export directly to Sketchup 2021
Rhino 6: Export to Sketchup 2019