There are two affordable ways to go to Modlin airport.
Method 1: 15 pln
First you have to go to the Pole Mokotowskie near the dorm. Buy a 20 min student ticket which costs like 1.7 pln per ticket. Near the ticketing machine look for the sign Centruum and follow it and walk up a flight of stairs. Then hop onto any of the tram (17,32,33,41) and take a few stops to DW Central, which is the Dominoes sign below. On the tram, you have to scan your ticket. But I usually ignore purchasing it and just ride for free. If the tram inspector catches me I will just speak Chinese and act very confused.
Once you reach DW Central, walk down the stairs and look for the train station. Purchase a ticket at the booth to the Modlin Airport (15 pln, check the timings here http://www.mazowieckie.com.pl/en/) and look for the platform to take it.
The train ride takes about 45 minutes and then you have to take a bus to the airport from the train station. No worries, the bus ride is covered in the 15 pln ticket.
Take a metro (5 stops) from Metro Pole Mokotowskie to Gdanskie. There, take a train from Gdanskie to Modlin train station. The train ticket costs 5.44 pln and you have to buy a shuttle bus ticket from Modlin train station to Modlin airport for 5 pln. Check the timings here http://www.mazowieckie.com.pl/en/
