Cheapest Flights From U.S. (NYC or L.A./S.D.) To Warsaw

Check out my answer in this thread. Basically your options are to:
1) take a direct flight (from NYC or Chicago - only with LOT),
2) take a connect flight with a regular airline (you might want to do some searches with momondo.com and skyscanner.net),
3) fly into a different country in Europe and take a cheap airline flight (check out the cheap airline hubs - London Stansted, London Luton, Eindhoven in Netherlands with easy travel from Amsterdam airport, Bergamo close to Milan, Stockholm Skavsta, Oslo Torp, Beauvais not too far from Paris and many more). All cheap airlines land in Modlin Airport (WMI), about an hour's travel from Warsaw. Cheap airlines include Ryanair, Easyjet, Wizzair and a few more. Watch out for luggage allowance.
4) fly into Berlin or Prague, or perhaps Bratislava and take a train or bus (if it's an ultrabudget trip). Berlin is 5 hours by train from Warsaw (3-4 trains a day).

Piotr1981 summed up your options in #1. I'll make three more comments:

1) If you choose to take a low cost flight once in Europe, read carefully the terms and conditions of the relevant airline in order to avoid unpleasant surprises and extra-fees.
2) If you purchase two separate tickets, allow yourself plenty of time between flights because if you miss one of your flights you'll have to pay for a new ticket on the spot which is (very) expensive. Don't forget to verify if the arrival airport of the first flight is the same than the departure airport of the second one and plan accordingly.
3) I would look to flights to Vienna instead of flights to Bratislava as they are more likely to be cheaper. BTW, there are direct flights from the USA to Vienna but there aren't direct flights from the USA to Bratislava.

Is it going to be OW ticket or RT? If RT how long you wanna stay? Right now you can get RT from JFK for around 650USD with Aer Lingus.

I'm going Round Trip thanks. but I also have to get to NYC from San Diego or LA.

Thanks for the tip.