The definition of "program" by WordReference.com is: "a sequence of instructions enabling a computer to perform a task; piece of software". However, it is not obvious for a human being that programs like Photoshop, Excel and our favorite video-game are all just a set of instructions. But, surprise: it is exactly what they are. Complex programs, such as the ones of everyday use in our computers, are composed by hundreds, thousands, or even millions of instructions. Even though there are people who spend a lot of time programming, most of these big programs are result of the effort of many people working together (and sometime code generators are involved, too).
"Sequence" is the other important word in the "program" definition. Following the same set of instructions in different order may lead to a very different result. For example, the mathematical operation " 5 + 4 * 3 " involves one sum and one multiplication. Doing one or the other first give different results: "(5 + 4) * 3 = 27" and "5 + (4 * 3) = 17". Similarly, if you are giving directions to a friend to go from his home to yours, only God knows where he could go if he followed your instructions in different order!
So, at the end, the mindset for programming consists basically on: understanding the goal to achieve, break it apart in small and individual steps, and translating them to the programming language we pretend to use.
Source:
Video lesson: "What is programming" in "Foundations of Programming: Fundamentals", at Lynda.com.