I would suggest to work on your software developer skills and math skills. I cannot speak to working at NASA (although that would be amazing!), but I would suggest learning what type of language NASA uses for their applications/software - then hone in your skills through constant practice and learning.
Is the job requires Computer Engineering or Computer Science- there is a big difference in these two majors.
Take challenging courses in your major and have high GPA - the employers will come to you vs you going to them.
Lindsay is right, in pointing out that the skillset is important to work on first. Imagine your software development skills as your toolbox — once you've gained the right set of tools and you've refined them, then you can take them with you and apply to any company.
In terms of getting into NASA*, it's all about having the right context. A successful NASA candidate should do their homework and have a strong sense of what problems their development teams are solving. NASA actually has a GitHub account where they show some of their open-source projects — give that a quick glance and you'll see what languages/technologies they're using.
In addition, it helps to do some research and become familiar with their working culture. Take some time to research their values and mission as well. This way you know how to shape your approach and you can bring in the right interpersonal/soft-skills, as you apply.
Remember Ryan, first work on acquiring the right toolset, refine your skills, then take them with you wherever you go in your career.
*Note — I do not, nor have I ever worked for NASA. However, learning about what problems any company is trying to solve, and learning about their technologies, is helpful in any job pursuit.
Randy recommends the following next steps:
Aside from studying Computer Science concepts to have the foundation to grow as a software engineer, I would recommend...
1. Apply for their internships. This is one of the best ways to get into companies.
2. Be able to obtain security clearance(s). Jobs with government agencies and government contractors will require ability to obtain clearances. Stay out of trouble, be a good person, make good decisions.
3. Apply for related positions / internships outside of NASA. If the space missions of NASA interest you, there are many other government contractors (i.e Lockheed Martin, Space X) that have entire departments dedicated towards space. Getting experience with those companies to then make yourself more marketable for NASA might be another angle to get in.
4. Visit Space Camps, Career Fairs, Summer programs where NASA is present and network.
5. Show and demonstrate interests that align with their mission and values.