In Final Draft 12, check the box at the bottom of the Welcome to Final Draft screen:
To access this window after the program has been opened, go to Help > Welcome to Final Draft.
In Final Draft 11, go to the Final Draft menu at the upper left and choose Preferences; check the radio button for Open Last Document.
Final Draft 10 / 9 use the Recent File function built in to the Mac operating system.
On OS X 10.14 (Mojave), 10.13 (High Sierra), 10.12 (Sierra) / 10.11 (El Capitan), 10.10 (Yosemite) / 10.9 (Mavericks) / 10.8 (Mountain Lion), go to System Preferences > General and uncheck the box for "Close windows when quitting an application." Adjust the Documents dropdown menu, if desired.
Note that this setting will apply to all of your programs.