In a single word, Experience.
To start, you need to have put in the ground work, so I can't recommend more highly that programmers should take the time to read books such as Refactoring, which will provide some of the more essential tools in a programmers arsenal that will improve your ability to maintain code, and Clean Code which has been written by some of the most highly recognizable talents in our field, and which describes nearly everything you need to understand in order to ensure your code is clean and readable.
No amount of reading however is a substitute for hard-earned experience. You really need to have worked with code for a while in order to fully appreciate the difference that attention to code quality can make. Through experiencing the pleasure of working with clean, well factored code, as well as the pain of working with code spaghetti, you learn to better understand what the authors of these books were really trying to teach you, but you do so in the wider context of real live production code, where the quality of what you do really matters, and impacts your ability to work easily with your code on a daily basis.
It also helps to have either a good mentor, or a peer with the experience to confirm that you are putting the effort into writing code to a high standard. This is just one reason why code reviews can be so useful. Using code checking and formatting tools can also be a very useful aid to ensure that you are keeping things clean. Nothing however compares to experience earned through years of writing software, such that you automatically find yourself writing code that is clean, readable, and structured simply for ease of maintenance, and all because you've made it a habit to apply best practices for so long.