In Gdansk, I used the local train service which was OK but nothing spectacluar.
Warsaw has a single metro line which is quite good, make sure you get the right entrance at the station as there are separate entrances for each platform and if you get the wrong one you'll have to pay again. Warsaw has OK trams, new s-bahns and I think double deck local trains. PKP mainline trains are generally bloody awful with the exception of EC and Express services.
To expand, on gordonthemoron's post, on the Warsaw metro, there are only separate entrances for each platform at Centrum (central station) and some stations at the North of the line (Slodowiec-Mlociny). At Centrum, if you were to use the entrance onto the wrong platform, you can go up to the next level using the lift and then walk across and then go down using another lift onto the other platform.
Buses made by Ikarus used to be very common in Warsaw and are generally popular among bus enthusiasts there, but they are becoming scarcer and scarcer as they are getting old and are not low-floor. If you want to see them, then peak times Monday-Friday are your best bet; they don't run at weekends though. Nowadays, the most common type of bus in Warsaw are made by Solaris. (Indeed these are common across all cities in Poland.)
Regarding trains, the SKM (S-Bahn equivalent), has roughly half-hourly services on lines S1 & S2 running through the city centre. These services call at Stadion station which has recently been redeveloped and is next to the Football Stadium. If you have a day ticket or longer, you can also travel on Koleje Mazowieckie trains within Zone 1. There are some Bombardier double-decker trains running from Warszawa Wschodnia-Radom (You can tell which trains are double-deckers as they all run via Warszawa Centralna). There are also Stadler FLIRT trains that run most services between Warszawa Zachodnia and Siedlce. Finally, the majority of Koleje Mazowieckie's fleet is very old and mainly formed on EN-57 trains.
Many of Warsaw's trams are really old, although they are in the middle of a big delivery of 186 trams from PESA to help modernise their fleet.
For general information, you need to buy your tickets before travelling. There are now many self-service ticket machines which have an English language option. You also need to validate your ticket before travelling either in a ticket machine on the metro or using a yellow validator machine. A Zone 1 ticket should easily be sufficient, but bear in mind, some routes (bus routes beginning 7xy or 8xy and train routes) go into Zone 2.
For the last few years, there have been lots of diesel loco hauled services from Gdynia to Hel and back in the summer period.
Not sure if these are running this year but it's a pleasant enough ride anyway, combine it with the ferry ride to/from Hel from Gdansk for a nice round trip out across the bay.
PS if you drink try the Brovaria pubs in either Gdansk or Gdynia, nice beers (Amber) and friendly locals....