How you ask for notes can be almost as essential as how you receive them. Of course, if you're writing on assignment or developing your original material with a producer (be it through a sale, option or shopping agreement) you will be given notes whether you ask for them or not -- at certain times in the process.
But even if you are working with a producer (or director), you should be willing to ask for notes when you need them, not just after deliveries.
Fortunately, asking for notes is simple -- and should be kept that way. Nobody wants to receive complex instructions on how you'd like them to give you feedback on your work.
You're Asking, Not Demanding
Politely, is the first and foremost requirement. Nobody is obligated to read your work or give you notes. They're not obligated to do so even if they already said they would, and they especially aren't if they're paying you (they can decide to pay you and never even read your work if they like -- it's their money).
Asking for notes from someone who is a professional (or accomplished pre-professional, such as a studious film student or avid self-producing filmmaker) is actually quite simple. You identify people who are willing to give you notes, and then you say "will you read this and give me feedback". Then they say either "yes" or "no".
What to Ask
If the person is not a writer, manager, agent, producer or director by vocation or avocation, they may not know how to give notes. You'll need to be more specific in what you ask them, without poisoning the well and accidentally guiding them into giving you your own notes back to you (you can also be specific in this way with more accomplished note-givers, but it's not necessary and may annoy some).
There are two simple questions which are the core of all notes requests:
Where, if anywhere, were you confused?
Where, if anywhere, were you bored?
A few more advanced questions that can be asked include:
Is as many or as few words as you'd like, can you restate to me what you think the script is about, both in terms of describing the plot (what happens), and the theme (the moral of the story), and how they fit together or fail to do so?
Who is the main character, what is their problem at the beginning of the story, and how do they change at the end of the story?
Each time you encounter a new character in the script, can you please list that character by name, and tell me what you thought of them at first -- and how that changes if you find yourself thinking more about them as you read on?
As you read, can you please write a rating number from 1 (worst) to 5 (best) beside each scene?
Essentially, those questions above are guiding your reader into writing development coverage of your script -- or at least the closest approximation thereof that an untrained reader is going to be able to muster.
Additionally, you can ask between one and five specific questions about the script overall (any more, and the reader will get distracted and either give up or provide you with much poorer answers to each). You want to be careful about picking those questions, and how you phrase them -- you don't want to write your own answer (or fear) into the question. For example, "Is this film too dialogue heavy?" is a much worse way of posing that question than "What are your thoughts about how balance between action and dialogue in the film?"
People are busy. Even people outside the industry. Even your mom and best friend. If you don't get your notes back right away, follow-up after somewhere between four and eight weeks. If your reader still hasn't responded after another four to eight weeks, ask once more -- then give up.
If they reply and say they're busy and will get you notes in the future, then patiently wait for the future. Someone I know got a call from a producer with not only notes, but a request to go forward on the project, one year after they sent the spec script to said producer in response to a query. If that writer had been desperate, they would likely have alienated that producer by pestering him and never gotten either the notes or the opportunity.
Naturally, don't just wait for the future. Keep working on other projects and pursue other opportunities. And if the people you asked for notes never give you any, find new readers.