If you look in the library panel, there should be an entry for your custom component - probably something like CustomComponent1.mxml. Drag this out onto the artboard to create a new instance of the component.
In the case of a custom component, you can't change much on the second instance. If you have something like a text input skin though, you can change the text it is displaying for each instance.
We are working on making this sort of thing easier in the future, so stay tuned
Hi there--you're right that you can't currently duplicate a custom component in order to change the text in another instance. We're planning to add this functionality before we release.
There's a simple workaround in the meanwhile: export the component (right click > Export Library Package) and re-import it (right click > Import Library package). This will create a duplicate of the component.