Say for example I made a cup, then made it into a component. Then I made 3 copies of that cup. Then I added a handle to that cup, and made it its own component. Having realized I should have made the cup and handle one component and made copies of that instead, I now want to make the two components (cup and handle) into one component, how can I do that.
If I explode the two components (cup and handle) and make them into one component then the copies will be orphaned. Is there a way to make the copies the same components without have to delete them and recopy?
Yes. You can use Edit>Cut to cut the handle geometry to the clipboard (explode the handle component first). Then open the cup component for editing and use Edit>Paste in place to paste the handle inside the cup component and it’ll show up in the other instances of the component.
PS: Use Model Info->purge unused to purge the original definition of the handle unless you will need it again for something else! Otherwise it will hang around in the components collection for no useful purpose.
Edit: a subtle technical difference between my reply and @DaveR’s: my way puts the base geometry of the handle into the same Component as the cup, whereas his way puts the handle in as a nested instance.
If you also want to do the same thing in reverse, i.e. get the handle out of the cup components so you can modify the different handles individually, or say move the furniture out of an apartment component to furnish identical apartments differently, I’ve made a plugin for that: Extension | SketchUp Extension Warehouse.