Arriving from abroad, you will probably enter Poland at Okecie airport in Warsaw (
Lodz does have its own passenger airport, but it is small, does not at this moment serve any international flights and is rather remote from the city center). From there, you may either take a direct express bus to Lodz (company Polski Express) from a bus-stop next to Terminal 1 (at the arrival level) or get to the Central Railway Station (Dworzec Centralny) in Warsaw and take a train to Lodz from there.
The express buses have limited passenger capacity and are often booked up. Visit the ORBIS travel agency office to buy a ticket immediately after having passed the customs. The office is located in the arrival terminal hall on the right when aiming the main exit just before the exit. One way ticket to Lodz costs ca 37 zl.