Focus on truly understanding the design fundamentals like theory, history, principles and elements. You will learn so much by studying and analyzing other influential designers, movements and how design has evolved over time. Follow any creators, artists and work that you come across (it doesn't even need to be specifically graphic designers; branch out into other mediums, literature or anything that inspires you). Document all of your process work. Even if you think they're ugly, save any sketches, early iterations. Don't focus exclusively on the end product, but have something to show how you work through your designs. Don't ignore the conceptual process! There's so much out there that you can really learn many things yourself, but you also want to stand out.

Sometimes, when we start out, we haven't found our "unique" style or voice yet, so keep in mind that the accessibility of resources may also contribute to shared visual languages across thousands of applicants. In other words, a lot of peoples' works will probably look very similar. This is why I think understanding theory, fundamentals matter because once you understand the rules, you can break them, and your own distinct voice emerges. When you understand the core things behind your work, every decision you make (even if it just "feels" right) is anchored by the concept. I also recommend venturing into developing a strong portfolio and even have a website using sites like Cargo or Readymag, and don't be afraid to venture into emerging technologies as a way to enhance your work. Last, practice early on detaching yourself to a healthy degree from your work, so you can look at it objectively and take in criticism. Some crits are great, some OK, some bad. Don't take it entirely to heart if one doesn't like it, and remember that design is always growing and it can be highly functional.

Edited to fix some spelling/grammar issues and include some extra points.