I dont know if you really mean Satmar or chasidim. Satmar are not really chasidim since they were in Hungary/Rumania and followed the Hungarian chasam sofer derech.
The derech of the first Satmar rebbe (and Hungarian yeshivot) was to learn what they termed 'sugya' shiur. That means about 3 topics what they considered in depth a term. They used to print out all the gemoros and meforshim pertaining to them. After they had learnt them the rebbe or RY used to give a shiur on them with his own chiddushim which have since been printed. As you know gemoro is rarely on one 'place' so they had to learn it from all over. Apart from this the Satmar rebbe when he was still in Rumania used to give a 'deep' daily morning shiur which was on the blatt and in the afternoon a quicker one. This was the method in all Hungarian yeshivot. Apart from this they learnt Shulchan Oruch with Magen Avrohom and others Yore Daio. There was a strict exam weekly which was also on the chumash rashi conducted by the rebbe in person. In Hungarian yeshivot they did not have 'classes'. There was mainly only one shiur given by the RY and the older boys used to have to learn with the younger ones (for payment).
This system has almost died out today. Although it is still kept in a minimum kind of way in Satmar. When the rebbe opened his yeshivo in America he still carried on given his 'sugya' shiur which as I say has since been printed but had hardly any listeners to it from his yeshivo since they couldnt keep up with it. But he did keep giving his strict exam weekly. He had a great sense of humor and when a boy said something wrong he usually made a joke out of it. One of his well known quips was that he had boy there whose name was moshe and his fathers name was Sinai. The boy made a mistake. So the rebbe replied, 'is that what moshe was 'mekabel' received from sinai.