Extract a Virtual Machine and boot from it

How do I extract a Virtual Machine of its Data, put that on a partition and boot from it?

Use the convert/dd subcommands of qemu-img to export and write the virtual image.
Combine that with losetup and partx to access specific partitions if necessary.
Then restore the bootloader according to the guest OS documentation.

Where is the Guest OS Documentation?

That would entirely depend on the guest