It's actually a lot simpler than the WikiVoyage article makes out, so no need
to worry! (I've now fixed that page...). The bus company website has changed recently, and the new timetable page is now http://www.plesoprijevoz.hr/zagrebzracna.html
If coming on foot from the city centre, your best be is to walk along Ul. kneza Branimira past the Graffiti wall, then turn onto Avenija Marina Drzica. You'll see the bus station on your right, and the Airport bus goes from the first building you come to in the bus station, which is white and labelled with
Croatian Airlines and Eurolines. Walk through the ticket office and out to
where the bus goes from. Pay the driver on boarding.
If coming by tram, take a 2, 5, 6, 7 or 8 to Autobusni Kolodvor (the bus station). Cross over to the bus station side, and turn right. Walk north
(towards the railway line) to the end of the bus station, with the shops on your
left. The very end part of the building is labelled with Croatian Airlines and
Eurolines, and that's the part you want.
If you need to change trams to get there, be aware that the stops at Drziceva are all a long way apart, so it's not a good place to change. Either get off there and walk (it's only a couple of minutes), or change at Olipska where the platforms are opposite.
The airport buses don't leave from the main part of the bus station, so if you're in there you'll need to exit down to the street, walk to the end of the building and enter the dedicated airport buses part there. It currently costs kn 30 one way, payable to the driver in cash on boarding. There are cash machines outside a few of the shops on the main road outside if you need them, and coming from the airport there's a cash machine inside baggage reclaim, and others in the main airport building.