Your save is kept on the server and written after every change; the Settings window is where you tune the game and where the account tools live.
1The settings window
MENU > GAME SETTINGS: the sections (1) run from Audio and Display through Battle & Autoplay to Account & Data. RESTORE DEFAULTS (2) resets only the section you are on.
2Account & Data
Your climb is saved on the server as you play - there is nothing to save by hand. Reset Progress (1) wipes this account's save and starts again at floor 1, level 1; Sign Out (2) ends the session; Export My Data (3) downloads a copy of your save.
3One window owns the save
Only one open window plays an account. Open the game somewhere else and the older window stops with a NOT SAVING notice (1): nothing it does is stored. Close it, or RELOAD (2) to take the save back.
Screenshots are taken from the live game by tools/tutorial_shots.py (dfmc-client) and regenerated after interface changes. The rules behind each screen: settings, system-client-shell, system-networking.