How do I update the firmware?

You do not have to. The ticker asks its server for new firmware five minutes after every power-up and once an hour after that, and when there is a newer version it downloads it over Wi-Fi, checks it, installs it and restarts. The whole thing takes a minute or two and shows Updating / Firmware with Keep me powered on! while it runs.

The only part that is yours: leave it plugged in whenever the screen says so. Everything you set is kept across an update. See Automatic firmware updates.