If you remember my second post in this series, I listed all sorts of things that a conductor must gain in terms of skills and knowledge. For the young conductor (or the experienced one, for that matter), many of the limits to your achievements as a conductor will be your own personal limitations as a musician. Your ability to hear what's happening in the music, to hear mistakes, to understand the structure of the music in terms of harmony and form--all these are a huge part of building your musicianship and of your ultimate success as a conductor.
As a college/university student, this means taking advantage of courses in music theory and ear training, but it neither begins nor ends there.
What happens before you get to college has a huge impact of course: if you studied piano or another instrument early on; were in choirs, orchestras, or bands; if your parents took you to concerts; if you studied voice; if you were part of an outstanding HS program with great training and experience in a fine choir . . . all of this is a part of your becoming a better musician.
But much of this background most likely came before your decision to become a conductor. So, given where you are when you begin college, take your own personal musicianship as far as you can.
As you begin your conducting career, this learning doesn't stop (note how that's an underlying premise of this whole series--becoming a better musician/conductor is a life-long task). You're no longer in classes (although you'll almost certainly attend conferences and workshops, and work on further degrees in conducting) but need to keep exploring and learning.
My own education after my Bachelor's degree was largely through the groups I started and conducted. While I'll talk more about finding opportunities to conduct later, the work I did with the Seattle Pro Musica ensembles--first a chamber choir, the 2nd year the Bach Ensemble (with which I did a Bach cantata once a month), and a chamber orchestra the last 3 years of my seven with SPM--preparing this repertoire gave me huge opportunities to improve my musicianship. At that time there were few Bach cantatas recorded so with many of them I needed to learn them from the score alone, figure out everything about how the music sounded, tempi, dynamics, etc. This work--and with the SPM groups I conducted 71 different programs in 7 years--was huge in increasing my level of musicianship. I've often said that the work I did with these ensembles was my graduate education. No matter what opportunities you have, use them to increase the level of your musicianship.
Later, when I became interested in the work of Eric Ericson and his choirs, studying and then preparing and performing many contemporary works pushed my musicianship in an entirely different way. Being willing to try to understand and then conduct much of this music was another part of my post-graduate education.
Besides improving musicianship in terms of your ear, understanding of harmony, form, etc. there is also the task of becoming a better interpreter. Again, some of this training comes from watching the conductors you work with (or others you hear live or on recordings) and seeing how they interpret the works you sing with them. But much will come from listening to and studying the work of a myriad of performers. How do great singers shape a song? Whether listening to a great Lieder singer interpret Schubert or Frank Sinatra sing a pop standard, there's a huge amount to learn about phrasing, rubato, how to shape text, and how to "sell" the song. What can you learn from a great instrumentalist playing a sonata or concerto? What about chamber music? How does a chamber group communicate? How do they play with great ensemble? And we don't only learn from classical musicians: how about great jazz artists? Musical artists of all kinds teach you an enormous amount.
In terms of understanding style--whether of a particular period such as the late Renaissance or of an individual composer, the same listening is crucial. To better understand how to interpret Debussy you need to have heard his piano works, orchestral works, chamber music, and songs. The same is true of understanding the work of almost any composer.
Listen (live performances or recorded), watch, listen.
How good a musician you become is largely up to you. It's in your hands . . . and ears.