I need to create a master artboard containing one or more other artboards to export work as sprites. However, the only way I can figure out how to do this is to create a blank artboard of the necessary size and then drag artboards into it. Is there a better way to do this - perhaps a keyboard or mouse shortcut?
Illustrator doesn't really have a "master artboard" option.
If you need one artboard which contains all other artboards, then you are going about things the proper way. Simply stack artboards as needed.
If you are looking for the ability to have identical items on several artboards, simply create the first item on one artboard. Drag it to the Symbols Panel. Then choose Edit > Cut followed by Edit > Paste on all Artboards.
The paste command will place the element in the same position on all artboards. If you need to then edit the object later, simply edit the symbol and all instances on all artboards will be updated as well.