I'm going to disregard your second paragraph, since a "modern-day" posek (your example was of the Mishna Berurah) doesn't go from the Talmud directly into halakha lema'aseh, but is already familiar with a great wealth of material that both predates the former and spans the two. For regular people, like ourselves, who want to gain a deeper understanding of the relationship between Talmudic dicta and contemporary halakhot, there are ways in which one can do this.
Let's assume that you are commencing with an individual sugya. The chances are that any Shas that you are using is going to have a useful index called Eyn Mishpat, which was compiled by a 16th century scholar named R' Yehoshua Boaz Barukh (known as the "Shiltei haGibborim"). That provides references to passages in the Rambam's Mishne Torah, R' Moshe of Coucy's Sefer Mitzvot Gadol ("SMaG") and R' Yaakov ben Asher's Arba'ah Turim. The latter work employs the same numbering system as R' Yosef Caro's Shulchan Arukh, giving you references to that corpus as well.
How you proceed from there is up to you. Personally, I prefer to use the Arba'ah Turim, since the commentaries of R' Yosef Caro ("Bet Yosef") and R' Moshe Isserles ("Darkhei Moshe") will give you a wealth of information that you can then follow up separately. Furthermore, since it employs the same numbering system as the Shulchan Arukh, you can proceed next to the Arukh haShulchan (by R' Yehiel Michel Epstein, a 19th-20th century scholar) and find references there to an abundance of material published after the 16th century. Similarly, if the material that you are looking at is in Orach Chayim, you can check the Mishna Berurah for the author's Be'ur Halakha, which is similar in scope.
If your interest leans more towards the Rishonim and the earlier period of Acharonim, I would advise checking the Mordekhai and (if what you are looking at is one of the masekhtas in which it appears), the Shittah Mequbetzet. The former was by the students of R' Mordechai ben Hillel (13th c.), and the latter by R' Bezalel Ashkenazi (16th c.). Where the former is a source for a large number of statements by Rishonim not recorded elsewhere, so too is the latter for early generations of Acharonim. Even more easily, you can follow Eyn Mishpat to the Rambam and check the commentaries there (Kesef Mishna, Hagahot Maimoniyot, etc).