You must be an NEHGS member to use the service. Membership starts at $89.95 per year, although there are options ranging into the thousands of dollars for life members, patrons, life-member couples, etc. who make a one-time payment. Those come with additional discounts on research & consultation and significant tax deductions. All members get free access to their enormous library & archive in Boston.
Option One is the all-inclusive service, meaning the NEHGS does everything for you that is legally possible (you must get your own birth certificate, for example), for a flat rate of $2,800 to $3,600 depending on your membership level.
Option Two, if you are not even sure if you have a qualifying ancestor, is to hire the NEHGS to evaluate your lineage specifically for a Mayflower ancestor. That costs a fraction of the all-inclusive service.
Option Three, if you just want help with a particular roadblock, their longstanding research service is available at hourly rates that vary by membership level. Actually, anyone can hire the NEHGS to do research, but members get discounts of $20 - $40 per hour. They can generate an analytical report along with the document if you have to plead your case to a lineage society. NEHGS's opinion carries a lot of weight due to the quality of their archival holdings and their research staff.
The arrangement they have right now is with the Massachusetts Society of Mayflower Descendants specifically, but you can inquire about having the NEHGS work with the state society of your choice. There is also the option of joining in MA and transferring or holding dual membership in a second state. I always recommend people join where they can actually participate in events and get a newsletter that has relevance to their own life.
To get started, go to the NEHGS web site, hover the cursor over the word "services" in blue and click on "Find the Right Service." (This connects to explanations of all their research services.) Or if you know you want their Mayflower Society service, pick "Services and Products" and scroll down until you see the option "Lineage Society Applications" and select that. Or you can just click here.
Good luck to you in search for your Mayflower ancestor!