This is repeating some of what has been suggested. The easiest way is a taxi, I know on the Black and White cabs website it will give you an idea of cost for your route.
For something cheaper, you could get to Portside with a shuttle, then catch a CityCat from Bretts Wharf. The ferry is around $4, you cannot use cash any more, need to buy a Go Card somewhere first. Translink website has a list of retailers - and no, they don't make it easy. From Riverside in the city you'd need to get to Roma Street which is a long walk. Note North Quay is not in operation yet after the Feb floods, same situation as quite a few other ferry terminals.
The airtrain is around $20 if you just rock up with a Go Card but family recently paid $28 for two adults, one way, from the airport to the city. There is a deal for two, maybe other deals on the website. Also cheaper if you prebook.