Poznań is crisscrossed by 19 tram routes (of which one runs at night), and 118 bus lines (20 at night). During the day these run from around 05:00 to 23:00 with trams and buses running approximately every ten minutes. Due to frequent track work and route changes, your best bet for figuring out how to use public transport in Poz is the super-helpful website poznan.jakdojade.pl (mobile app also available), which can tell you exactly how to get from point A to Point B in English.
Transport tickets are bought from automated machines found on most buses and trams, as well as at most transport stops, and the fact that you can pay by card means you don’t have to stress about having change. The galaxy of ticket options travellers are presented with is far too complex to review here; you can take it to heart that you won’t be leaving ‘Zone A’ unless you’re travelling far outside of the city-centre, as even Lake Malta is within Zone A. Tickets are timed, and the cheapest option is a not-very-cheap 3zł for only 10mins - which might only get you 3 or 4 stops. A 40-min ticket for 4.60zł is the safer bet, but if you plan on travelling often, you may want to consider a 24hr or 48hr ticket. Another option if you are here for a few days is the Poznań City Card which gives you free unlimited use of the public transport system as part of the price. It’ll save an awful lot of headaches. Note that kids under five and adults over 70 ride for free.
Finally, it is extremely important that you remember to validate your ticket by punching it in the ‘kasowniks’ found by the bus/tram exit as soon as you board. If you don’t have a valid ticket and find yourself nicked by a plain clothes inspector you’ll be fined 140zł on the spot as well as the cost of the ticket you didn’t purchase/validate; and if you don't pay within seven days the fine jumps up to 280zł. Yes, Poz public transport is a bit of a racket.