Good morning Naomi,
How to file suit is the $64,000 question. If you are not an experienced litigator, you would be much better off having a local family law attorney file the petition for you. You are much more likely to have it done right the first time, and begin getting the support payment sooner if you have experienced help.
But yes, even while you are separated, you have the right to seek spousal support.
As I suggested, you would be much better off having a local family law attorney do this for you---but if you have more time than money, you can try and do it yourself. Virtually every county has a law library. Ask the law librarian to show you where the books on Pleading and Practice are located. Generally there are many volumes of Pleading and Practice books from which you can pick the proper one for your situation. While the librarian is typically not a lawyer, and cannot practice law, most are quite willing to assist you in locating the chapter in the Pleading and Practice book which you will need.
Once you have found the appropriate pleading, you will note that in addition to the sample pleading which contains all of the necessary structure for your Pleading, there may also be suggestions to make your pleading more persuasive. Prepare your pleading in accordance with the suggested format in the book, inserting the facts of your case as you know them to be. Then all you will need to do is to draft the pleading on your computer, print it out and file the original with the court while serving the other party, or their attorney, with a copy.
You may reply back to me again, using the Reply to Expert link, if you have additional questions.
I wish you the best in your future,