How to edit a Profile shape used in an Assembly

Follow these steps to modify the shape of a profile used inside an Assembly:

1. Build a section of the assembly and (using the Select tool) double-click it to edit.
2. Double-click the Profile Member that you want to edit.
3. Click the 'Edit Profile' button in the main toolbar (Edit the Profile of the Active Profile Member)
4. Edit the profile shape using the various SketchUp tools as desired.
5. Click outside the profile shape to complete the edit.
6. Now inside the assembly dialog, click the large button that is labelled with the profile name which will activate the profile picker tool. 
7. Click the profile member that you just edited in the viewport. This will update the profile used for the assembly (stored in the dialog) to the edited one that is in your model.
8. Now when you click the assembly build tool, it will build with the edited profile.

Rather than editing the shape, if you want to replace the profile entirely, or modify the various attributes, it is better to click the profile icon button to open the profile dialog which will allow you to modify the attributes or load an entirely new profile.