You are right, most trains need about 1.5 to 2 hours from Warsaw to Łódź. It's best to check connections on http://rozklad-pkp.pl/bin/query.exe/en? (from: Warszawa Centralna to: Łódź Widzew. Trains used to go to Łódź Fabryczna station which was near the city center. This station is currently being renovated and it wasn't listed on PKP's website so I suppose that all trains terminate at Widzew now. But I am not so familiar with Łódź so it would be better if someone here on TA could confirm this information.
Internet booking usually works fine. There are also some ticket machines at the main station in Warsaw. Those for credit card payment only are located in the underground passage (it's not easy to find them) but there are also machines accepting cash: outside the station next to the bus stops (on the way to the shopping mall). Polish railways employ many older ladies who do not have any knowledge of the English language. You can also write down or print train information (direction, time, type of train e.g. TLK, class) what would make it much easier. Or you can asl people to help.
TLK is not the company name but the type of train operating. Beware that TLK trains usually leave a lot to be desired in terms of comfort and cleanliness.
Warsaw has several big stations but the only one in the city center is Warszawa Centralna. It's located in the heart of modern Warsaw, next to the Palace of Culture.