I'm using the CS50 virtual machine and installed Dropbox. I couldn't find my Dropbox account in home directory the next time I logged out and powered off the appliance. How do I restart the appliance? Is the appliance launched through VMware Player every time?
Yes, you must open VMware Player to run any virtual machine, including the cs50 appliance.
If you are looking for a Dropbox folder on your computer, outside of the virtual machine, make sure you have installed Dropbox in both places - on your computer, and inside the virtual machine - separately.