How does NASA hire software engineers?

NASA doesn't really have a large organized recruiting department. Sourcing is normally done completely independently at each center, (exceptions being cross-center programs) and often within a center independently to each lab and program. While grant-based labs could technically set aside a recruiting budget, most of them do not, and there is a fair amount of blood spilled in poaching somebody already within NASA to another lab. JPL, as always, is an exception to this because they cherry pick which rules to follow juggling between their statuses as a NASA research center, an FFRDC, and various other things they can do under the name Caltech. If you want to get into NASA, have American citizenship and are a student at a 4-year university or a grad student, your have probably 60% odds (there are a few 2-year schools in the program, but not many) of having your school be in the Space Grant Program. Look up the program for your state, call up the head office, and see if you meet your state's requirements for a space grant. If you don't, and you are attending your college from out of state, check your home state's office (very rarely it works.) Then you can call up pretty much any NASA lab at any center and tell them you want to work for them, and somebody else is cutting your paycheck. They will almost certainly take you unless it is JPL, because there is very little predicting any of what JPL will do (aside from living up to the Just Pay Lockheed backronym). If you are not currently a student and want to work for NASA, I would advise you to see if you can cozy up to a base socially and see what postings are available for labs in that division, or if that is not logistically possible, see what postings are available through the 3rd party companies which provide what are called contractors to NASA. Since all employees are either legally contractors or civil servants, a dozen or so large companies (and many more small ones) have popped up for the sole purpose of interfacing the employees individual NASA labs have selected to hire to payroll and benefits. They will not be involved in your hiring at all, they will just show you where opportunities are. If you are not an American citizen or do not have a degree, get fostered in and vouched for under one of the many universities which has an on-campus presence. Good luck, you are fighting a very uphill battle. If you are not an American citizen, your odds are confusing. Some countries are easy, and some are hard. Which countries are easy to get in from and which are not is not intuitive to most folks, as it is way easier to get clearance for a German or Spanish citizen than it is to get a Canadian one. As a rule of thumb, short of being from a country the US is openly having a conflict with, the easier it is to become a citizen in your country the harder it is to get clearance to go over the fence. This is because people of a dated fear that an enemy will use positive relations with a US ally as a privilege escalation exploit by becoming a citizen in the friendly country then stealing the details from all the military hardware which is also used at NASA. tl;dr: NASA doesn't have a central system for hiring, and the methods are kinda a mess. There are a few exceptions, but you generally apply for each job in each lab individually.

I was hired by NASA through OSSI (https://intern.nasa.gov/) which is a shopping-cart like website where high school, undergraduate, and post-graduate students can apply for NASA internships. The website lets a student apply for a maximum of fifteen internships per application season--they have summer, spring, and fall seasons corresponding with the typical academic year. There are also year-round internships available that would span more than one semester of school. Being available for year-round internships will make you more competitive in the applicant pool. OSSI requires a letter of recommendation. I was fairly new as a college student at the time of applying, so I had one of my high school teachers write the letter of recommendation. My strongest points in the application were knowing a wide variety of software languages and technologies and a good amount of experience through past internships. I was phone-interviewed by several the leaders for groups at the Kennedy Space Center--but ultimately I chose to take a position with the Intelligent Robotics Group at the Ames Research Center. A few of my interviewers at Kennedy stated that they had started at NASA as interns themselves, so the intern process is an intelligent way of getting your foot in the door. Many of my coworkers at NASA Ames worked as contractors, and that would be the best way to get in for students outside of a high school or a university setting.

http://www.usajobs.gov

Also, their PR success in popular culture has been quite impressive, as considerable prestige is now afforded to those deemed to have expertise in "rocket science"

At Ames, most of the software engineers are hired through contractors. So, it's best to search for jobs through the web sites of contracting firms. For the Intelligent Systems Division (Code TI), the primary contractor is SGT (http://www.sgt-inc.com). For the Advanced Supercomputing Division (Code TN), it's CSC.  Here is a link to the complete list of contractors at Ames: http://amescontractorcouncil.org/NASAAmesContracts.pdf