What is the exact meaning of "actually" at the beginning of a sentence, followed by an imperative, like: Actually write down the rules.
Edit: More context: The writer who has written this sentence has previously said that writing down rules is important.
This is how I would interpret that flow of thought.
Writing down rules is important. Actually write down the rules.
The word "actually" is included here because people might be tempted to think the recommendation doesn't apply to them. They might think to themselves, "Maybe other people should write down the rules, but I have a pretty good memory, so I don't really need to." The author is saying to that notion: "No, don't just think about writing them down, or consider writing them down, or put writing them down on your to-do list, actually write them down." In this context, the word actually means really, but it also functions as a strengthener; it makes the directive stronger.
It's interesting that, among the several definitions listed at Wordnik, two of them fit this context:
actually (adv.)
as a sentence modifier to add slight emphasis
as an actual or existing fact; really; in truth: often used as an expression of wonder or surprise: as, he actually accomplished what he undertook
I think these two definitions in tandem explain the meaning of the word rather well.
It indicates that the person giving the order just changed their mind, and now wants the other person to do something. For example, if I had previously said not to write anything down, but changed my mind, I would say 'Actually, write down the rules'.
Note that it is always followed by a comma in writing and a slight pause in speech
