As an alternative, you can also get an Epping line train and occasionally an Eltham/ Hurstbridge line train from Flinders Street, Southern Cross, Flagstaff (F closed weekends), Melbourne Central or Parliament stations to North Richmond station.
Epping trains almost all stop all stations from Jolimont to Clifton Hill including North Richmond; the Eltham/ Hurstbridge trains mostly run express.
A map at www.whereis.com.au should show you where these stations are if you do not already know.
Like the tram, North Richmond station is in Zone 1.
On Sundays buy the cheaper Sunday Saver from staffed railway stations, 7-11s, chemists. newsganets and so on; other days buy a Zone 1 daily or two-hour ticket: the latter two types are available on board trams and buses, and also at Metcard ticket vending machines at all railway stations. A two-hour ticket, if validated at say 1301 is then valid for your last boarding before 1600 (rather than 1500) as the 'next hour' is used (i.e. the two hours commences clicking at 1400 in that case), and there is the additional rule that if you are at the railway station or tram stop at say 1555 and the next scheduled trip is not until say 1605, you can board that service and travel to say Collins Street.
Fares and timetables are at www.metlinkmelbourne.com.au, or timetables at www.yarratrams.com.au and www.connexmelbourne.com.au