People have been accusing Trump of not even reading the executive orders he signs. This begs the question, who actually writes them? I always thought that the president was the one who wrote the orders, either by himself, or working with advisors.
That makes no sense at all. Why would any president sit down and type out an EO when he has a staff of hundreds?
The White House staff (meaning people within the Executive Office of the President) write them.
Usually, they do this in consultation with the legal officers in the departments or agencies that will be affected by the order, to ensure that the order is legally defensible and fits coherently within current statutory requirements. This also ensures that the agencies affected will have time to prepare themselves to implement the order and write the necessary guidance for their staff. Famously, this process was largely skipped with the recent immigration ban kerfuffle, where the order was largely written by Trump’s inner circle and not vetted by anybody for legal coherence or practicality.
It’s probably not reasonable to expect a president to read every word of every EO that he signs, just like legislators aren’t going to read every word of every bill they vote on. But it’s reasonable to expect them to be broadly familiar with the order’s goals and effects, and it’s reasonable to expect the president’s staff to draft them using a competent process.
Ok, I can see that “the President, working with his advisers, writes executive orders” is a reasonable assumption, since the fact is that his staff and the agencies under him do indeed write them.
But you assumed that the President writes them himself? I’d suggest that you read a few executive orders – they are really, really dense reading, often much harder to read than laws. You can click around and read some here — no way that a single person just pounds them out sitting at their desk in front of Word 2007.
https://www.federalregister.gov/executive-orders/barack-obama/2016
That was then, this is now. 
True. Presidents don’t write the text of executive orders. They have somebody like Josh Lyman who does that kind of work.