There are various methods and points stressed by the diverse various schools of Torah learning. In Telz, they do "Chakira" - analyzing each case how and why certain laws apply to it, thereby arrive at conclusions from Talmud, and apply it to other cases. It is a slow learning process, which suits a person who is very deliberate in his studies.

In Brisk, it is the understanding of Rishonim, especially Rambam, that counts in analyzing what is said in the Talmud. "Chakira" method is also applied, but mainly they search for the underlying reasons and word selection of Rishonim.

"Pshat" was very much stressed by "Chazon Ish" looking for the most straightforward reasons for matters. This method also has a keen interest, in summarizing each passage in Talmud, as to its practical application in Halacha, and its development toward the final Halacha as we have it today.

Whatever method is chosen (and there is lots of overlap between the methods), the aim should be to have at least a general idea how the Gemara leads to the final Halacha. The diverse methods help keep different minds (young, old, mediocre, sharp, etc.) interested in Torah study, which is in itself a mitzvah. The ultimate goal is its application to Halacha.

Some famous Rishonim: Rashi, Rif, Rambam, Ramban, Ran, Rosh, etc.

Achronim: Ketzot, Noda B'Yehuda, R' Akiva Eiger, Gra, etc.