When you reach Warsaw by plane, the most convenient way to get to the city centre is to use the rail link. The railway station is just next to the Terminal A. Travel from the airport to the city centre takes around 25 minutes. Of course you can use also a 175 bus or a cab, but the train gives you immunity to the Warsaw car traffic.
When you arrive to the city centre you can walk to your hotel or you can use public transport. If you are going to use the public transport a lot, it is convenient to buy a period ticket which allows you to use buses, trams and metro. A great is that you needn't care about zones - you simply buy a ticket for zone 1 as zone 2 is really far away and you needn't go there.
You can buy tickets in ticket machines or at newsagents'. A good way to find public transport connections is to use a webpage:
Please note that this search-machine offers you just to pick a point from the map and it finds how to get there from any start location. It has the google engine and is really user-friendly.
Iam sure that in the internet aeon there is no need to paste old fashioned maps - just use this ZTM site and google map or your gps and for sure you don't get lost.