It depends on the type of non-profit org. For example, congregation/church and few other types are done slightly differently.
Most of the charitable orgs are considered non-profit corporation and one must register the non-profit corp with the state the org is located in. Therefore, expenses related to this registration varies by state. (Some states are easier, others are more complicated)
Corporation should be a non-profit corp created under the specific laws of your state. There are various services that will create a corporation for a minimal expense, but it is far too easy in some states to simply do it yourself. Your best source of information for this is your Secretary of State. (Search for your state's Non-Profit Articles of Incorporation)
If your final goal is to become a charitable organization recognized by the IRS then you will want to be certain that the language on your Articles of Incorporation meet all of the requirements. (IRS Publication 1828 http://www.irs.gov/pub/irs-pdf/p1828.pdf
You will generally need three individuals that reside in the state to be the Incorporators and/or initial Directors for your corporation. The same three used to create your initial congregation are normally used, but not necessary.
Although the Secretary of State may assist you with this you cannot be certain that all is necessary and proper for future use with the IRS. You should really consider using an attorney to at least look over your forms before you file them.
Finally, you will need to get a tax ID number, commonly called an Employers Identification Number, EIN, or Taxpayers ID Number. For this you will need IRS form SS-4.
Again, details of registration might be slightly different depending on where you are. I am a CPA licensed in NY State only. Also, I only practiced taxation (specialized in real Estate) for only about 1.5 years.