You have received some excellent advice from others. Directorick is right about finding low cost editing services for proofreading. If you have a friend or family member who is that spelling and grammar whiz, take advantage of that fact. As Rayw mentioned, this only is a major issue if you are trying to sell/option the script to someone else to produce. Most can overlook an infrequent typo (once in 5 pages). It is when you have one or more on each page that readers tend to throw up their hands.
Scripts will go through many re-writes, pro or not. So don't sweat the first draft. Just write it. Once it's finished, then go back and clean it up. It's in the second pass that I usually catch many of my mistakes. It helps to have a dictionary and thesaurus next to where you write. (Is it "breech" or "breach" I want? Since both are English words, the spellchecker doesn't help I found out.)
It is easy to spend money in pursuing a dream--contests, evaluations, listings, printing and binding, etc. So if you can find no cost or low cost proofreading service, all the better. The services which BrianLuce and I mentioned include evaluations of how well the dialogue works, character and story development, in addition. Neither of us are suggesting that you need or should use those services. We mention them so you are aware they exist, and what you might expect if you go searching the Internet.
I would write stuff like that down so i wouldn't forget, and i have been playing this movie over and over in my head for years... Isn't that crazy? With that said, I've never done anything like this (SCREENWRITING) and i was wanting to know a few things before i get started.
At this point it is often called a "treatment". A treatment is a 3-30 page presentation of the story largely without dialogue. This is a good place to start before you tackle the script itself.
Having said that, I'm going to give you advice that most first time screenwriters do not heed or want to hear. And I'm sure others here will disagree. If you are the director, the script is largely irrelevant except for the actors and crew. Regardless of what's on paper, you are creating your story in real time as you imagined it. If it doesn't work, you try again--a trial and error approach. However, if you are only a writer, your script is held to a high standard to warrant consideration for production or financing the creation your picture. In those cases, I would want my script to have a good chance at success
if I've never written a screenplay before.
In your place, I would write down my movie as it plays in my head in a story format (treatment). Don't worry about the screenplay part at first.
Now set it aside. Many beginners anxiously rush to write a script without preparation. The result is often rejection. Most first screenplays are never produced unless the writer is also the director and producer. I think it's more due to the learning curve than the idea itself.
I would pick up a book on script writing at the library. Everyone has favorites. I would suggest a book by Hal Ackerman, "Write Screenplays that Sell the Ackerman Way". It covers the basics of the "Three Act Model" and helps you think about structural aspects of the story. I don't agree with everything he writes, but it is a very clear, easy read with exercises. Create a short film script from the exercises to understand the principles. David Trottier's book "The Screenwriter's Bible" will help you learn the formatting. [NB: There is nothing 'magical' about Ackerman's approach, it's just a practical, hands-on approach. I also like Michael Hauge's approach. Blake, Field, Seger, et al. have instructive approaches as well. I would give them all a read to get a wide sense of approaches to the good screenwriting.]
After you've written a couple short scripts (5-10 pages),
read successful movie scripts! Go to SimplyScripts, Imdb or other places on the internet to read scripts of movies you really like. It can be eye-opening and instructive to see how they wrote and scripted their ideas.
Now that you know how to structure a good story, how to format your script, and have seen how successful movies have structured these elements, you should pull out your original story treatment. How will you capture the audience in the first five or so pages? How will you introduce the audience to the characters and create the driving force for the movie in the first 20 or so pages? Unlike a book, a movie has a limited number of pages to tell its story, so it needs to be given thought. The characters need to feel real to the audience. There should be movement and development from start to end.
If I had this marvelous piece of marble and a brilliant conception but I'd never carved before, I'd want to start with scrap rock and simple sculptures to develop my technique. When I felt comfortable, then I'd start on the actual piece. I think most first efforts are the same. Having an awesome imagination and a knack for flowing things together, you should have no problem applying this to smaller pieces to master the skills for a feature film. Practice then tackle the story with some mastery.
In the thread that PolFilm posted there are some thought provoking links. There have been other threads on this Screenwriting forum that have addressed many of the issues of story, structure, and format. The 'trinity' forms the basis for scripts. If any one is weak, the whole script suffers. When all three work well, the script succeeds. Good luck in your endeavors.