If you are a foreigner outside from the EU, it is possible to drive in Poland with an ‘International Driving License’ during your first 6 months in Poland (provided that you always show you national driving licence as well). Should you want to get the Polish driving licence, you will need to go to the Driver and Vehicle Department (Wydział Komunikacji) of your place of stay. Check the procedure and requirements here (for Warsaw).
The above mentioned procedure applies to EU & EFTA countries, Switzerland and countries which signed Vienna Convention of Road Traffic (full list of countries here).
Information for Mexican citizens
Legally speaking, Mexican citizens cannot drive with a Mexican driving license in Poland. In general, citizens of the countries that signed an international treaty called the Vienna Convention of Road Traffic may drive in Poland with their national driving license during the first 6 months of their stay. However, Mexico did not sign the convention, which means that Mexican driving license is not valid in Poland. It also means that if you are a Mexican, a legal requirement to obtain a Polish driving license is to pass a theoretical exam. This is an official procedure, however, depending on the office which you go to, the procedure may vary (some offices might exchange the Mexican driving license for a Polish one without asking you to pass the exam).
In order to apply for a Polish driving license, you must prove that you have been in Poland for at least 185 days. You should go to the Driver and Vehicle Department (Wydział Komunikacji) with your national driving license. The Department will then take your driving license and start a procedure in order to confirm that it is valid and authentic. This may take from 1 to 3 months (however, it can never be predicted).
After you receive the information that the procedure has been completed, you should go again to Wydział Komunikacji and pick up a document called Profil Kandydata na Kierowcę, with which you should go to your Voivodeship Training Centre for Drivers (Wojewódzki Ośrodek Ruchu Drogowego) and make an appointment for the exam. The exam may be in English, however, all the instructions before and after the exam will be given in Polish.
And mind: Polish driving rules may be difficult for foreigners and the exams are getting more and more tricky. Make sure you solve some sample exams in advance.
To check details of the procedure and requirements, click here (for Warsaw).