Walk the centre. It is about two kilometres across and flat, and you will walk almost everything.
Trams are run by ZET — blue, fifteen day lines and four night lines, and nearly all of them pass Ban Jelačić Square. If you are lost, get on almost anything.
Tickets are a flat fare for a set duration, bought from a kiosk or machine, or from the driver at a higher price. Validate in the yellow machine when you board — an unvalidated ticket is no ticket, and inspectors work the lines.
Day and multi-day passes exist and are worth it from about three journeys.
The lines you will use: 6 for the main bus station and Novi Zagreb; 14 for Mihaljevac and Medvednica; 11 west along Ilica; 5 or 17 for Jarun; 11 or 12 for Maksimir. Bus 106 from beside the cathedral for Mirogoj.
The funicular is a separate fare — a ZET ticket does not cover it. It costs almost nothing and takes 64 seconds.
The Upper Town is cobbled and stepped. The Grič Tunnel is the flat, step-free route between the levels.
Taxis. Uber and Bolt both operate and are usually cheaper than street taxis. Local firms are reliable and app-bookable.
The airport is 30 minutes by shuttle bus to the main bus station. There is no train. See Zagreb Airport to the city.
Do not drive in the centre — parking is zoned and enforced, and much of the Upper Town is restricted. A car is useful for the Zagorje and Plitvice and nothing else.
The full version is getting around Zagreb.