What should I try to learn before showing up at BLC?

I assume you're going to the BLC at Camp Cook, LA.

Have you looked over the Academy's website and accomplished the tasks laid out in the welcome letter* that was (or should have been) sent to you? Have you ensured you have all the prerequisites accomplished as well as documentation you'll need to arrive with?

The Academy has a student's guide (part of the welcome letter link) which gives an overview of the three weeks you'll be there, what you'll be focusing on, etc. On that same page, you can bring up the training schedule which will go into a day-by-day laydown while you're there.
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* Camp Cook BLC Home page - https://www.campcook.page/home
* Camp Cook BLC Welcome Letter - https://www.campcook.page/welcome-letter

SPC (Join to see) Review the Leadership Requirements Model and Troop Leading Procedures. You don't have to be a subject matter expert going in, but it is always good practice to try to find out where your knowledge gaps are and where you may need more understanding.

Remember that they are preparing you to take responsibility for 4-5 junior enlisted Soldiers upon promotion. This course is designed to develop you so that you gain the knowledge, skills, and abilities to develop others as a Soldier and Infantrymen.

I would reccomend pay special attention to effective counseling instruction. You should be ready to be able to knock out a verbal counseling on the spot that mimics formal counseling. For example, when you are counseling a Soldier you tell them why you are talking to them, what is the relevant guidance that prompts the conversation, what the plan of action is, and what their questions are.

Too many young NCOs focus on writing everything down and while some instances of "making it official" is required, not every interaction needs a stack of paper. As you gain experience and guidance you will know what needs a formal sit down. Rule of thumb for most cases of "developmental counseling": tell them once, second time write it down, third time send them to Squad Leader.

The Leadership Requirements Model highlights exactly what leadership attributes your rater should be evaluating as you develop as a leader. Understand the NCOER and what your rater expects to see from you that meets the standard and ask them what it would look like to exceed the standard for every evaluation area.

Don't forget that upon promotion, you are 11B Skill level 2. Grab the STP 7-11B4 and understand exactly what that means.

Final thought, junior leaders will sometimes emulate the leadership attributes of the leaders they have been exposed to that they think are the best attributes to have. 9/10 times they emulate the behavior of a toxic leader or a drill sergeant. Don't do that, find your own way. Remember the NCO creed: "All Soldiers are entitled to outstanding leadership, I will provide that Leadership."

Great question and the answers posted are good. Here's a different challenge for you. Know the job two positions higher than you -- hands on, responsibilities of the job; the administrative paperwork aspects of the job, the regulations and resources of that job {Army, Installation and unit}. With that knowledge you'll have no issues with schooling.
My last thought on BLC (PLDC) -- it was my 1st time to wholly interact with MOSs outside of my unit -- there is a lot to be gained from how the different organizations "do the Army" - Combat Service Support, Combat Support, and Combat - each other student is a lesson - good, bad, and yes ugly.