The safest - though not cheapest option is to stick to Taxi MPT in Warsaw. The have the best cars, and the girls on the phone speak english (even some drivers - if they are in a good mood :-)To order just dial 919 (from your mobile 022 919) - though you usually find plenty of them at the airport, the Central train station, and around the city.
(Yes, sometimes the girls of the other companies do speak English too ... though you can not rely on it ... yet)
In case you need fast and reliable way to get somewhere ASAP or you are just tired of getting on the wrong bus or tram that takes you into unknown, hop on the cab that should take you to your destination.
For Western standards cabs/taxis are pretty cheap here and you can expect to be charged PLN 5 + (PLN 1.4 to 2 per kilometer), that converts into around less than USD 10-15 at night in the downtown and its close outskirts. Of course the prices refer to honest cab drivers (I prefer two corporations -MPT (call 919) or Extra Taxi (call 96 83)). Beware of some scalpers that happen when you take taxi straight from the street in most touristy or nightlife areas of Warsaw.
You can take a taxi. Please remember to call for one by phone, never pick it from the street unless you want to be cheated.
There is no extra charge for ordering a taxi by phone.
The standard charge per kilometer is 2 PLN, which is about 0.5 EUR. Below you will find information on my favourite taxi company in Warsaw - they charge only 1.30 PLN per kilometer and have good cars (no hidden catch).
When I am in a strange city, I feel much safer when having a number to a taxi company I can rely on.
In Warsaw of course they have planty of them, but I do remember one with an easy telephone number and nice staff :-)
TAXI SAWA +48 (0)22 6444 444