I can speak to this issue as someone who comes from a formal background of philosophy and literature, but whose work involves a lot of programming (both reading and writing code) at this point.

Foremost: practice. If you can read and write essays at a college level you've been practicing the craft for (likely) years. Most educated people in the US start engaging with letterforms as soon as kindergarten (!), and no later than 1st grade if not preschool. Contrarily, we don't start so early with the rules of logic nor programming constructs. Most folks don't start programming until much later, and even those who are precocious in this regard usually don't begin using "real" languages (in other words, not stuff like lego robotics or scratch) until they are ~13 or so (of course, there are plenty of exceptions). As with most skills, practice is invaluable.

On a conceptual level, I found that making the jump from asking myself what does this code do to what does this code mean majorly beneficial. It may seem like a minuscule or pedantic semantic point, but it actually makes a world of difference. Just like essays, programs are expressing—they are saying something. If you shift from approaching programming from a goal oriented perspective to a communications perspective your code will probably improve immensely. I think this is the reason guys like Donald Knuth stress code readability and literate programming so heavily—at the end of the day, that's what's really important: communicating some idea—just like we do in plain old english. We simply have a broader audience (the latter part of which is very picky about what it understands). The notion of a proposition in logic doesn't do, it means. Programs are essentially a set of propositions which just so happen to have the side effect that they can make a device (a computer) do something when it interprets them. Just as linguistic commands ("go to the store") are "pure" and free of side effects in and of themselves—they only have effects under human interpretation.

On a somewhat related note, I find stepping away from programming languages and starting with pen and paper is great. I think people tend to let programming languages get in the way of the real nature of what it is they're doing, which is solving problems in a structured manner, using mathematics and logic (algorithms and data structures). You don't need a programming language to do this, it's only a vehicle to express your solution. Just as you'd often start writing a formal paper by exploring your ideas in an outline or notes, or a couple of first drafts in which you hash things out, you can start "programming" by sketching ideas for solutions and better comprehending the problem at hand. This will ultimately help you write better code. I think a lot of self-taught devs, such as myself, miss this part early on as our entry point into the discipline is often through the languages and tends to kind of remain at the level of the languages we like unless we dig deeper into the underlying formalisms driving them. Too often people just go along with their first-pass understanding of a problem and begin reaching for the libraries, language constructs, etc. that they think they need. Someone with formal training, contrarily, has professors that can help them recognize the concepts behind the languages and connect up and distinguish the notion of a language as a mode of expression and programmatic problem solving as a practice irrespective of the selected language.