The Trensurb metro is the backbone of public transport in Porto Alegre. It runs from the airport south through the city centre and out to the northern suburbs — a single line, but a useful one. Buy a reloadable card (Cartão TRI) at any station; it works on both the metro and the city buses. The fare is cheap by any standard, and the trains run frequently during the day. For the city centre and close-in neighbourhoods like Moinhos de Vento, Bom Fim, and Cidade Baixa, the metro combined with walking covers most of what you need.
The bus network is extensive but complicated in the way that almost every Brazilian bus network is: many lines, numbering logic that only makes sense after you have lived there a while. The Moovit app handles Porto Alegre well and is the easiest way to navigate it. Taxis and Uber are both readily available and reasonably priced by European standards — useful for getting to the Fundação Iberê Camargo or the football stadiums, which are a bit far to walk. The city has been expanding its network of cycle lanes (ciclovias), and the flat waterfront and Centro Histórico are pleasant to cycle. Bike-share schemes operate in central neighbourhoods. Driving in the city centre is not recommended: parking is expensive and the one-way system confusing. For day trips to Gramado, Canela, or the wine country, renting a car from one of the airport agencies is by far the most flexible option.