We are a group of researchers in Europe, interested in filling a provisional application for a patent regarding a device that we developed.
What is the cheapest, fastest and more effective way to do this?
Cheapest is to write as complete a description as you can, include drawings that the text makes reference to and then fill out a provisional application cover sheet. Either mail it all to the USPTO or file it electronically using EFS-Web I suppose the fastest is to do the above but use whatever description you already have created - maybe a PowerPoint presentation. Of course these approaches may not be the most effective.
To be most effective I would definitely get advice from a US registered patent practitioner. Although it is said that provisional applications have few formal requiremnts, if it ever actually comes into play as something you are relying upon, the sufficiency of its content will be judged under 35 USC section 112, exactly by the same criteria the content of a "regular" patent is judged.
Having it drafted and filed by a professional is highly recommended.(yes, I am one) Someone that works as a solo practitioner or in a small practice might be more oriented to cost-sensitive inventors.
If your only goal is to obtain a (so-called) priority date which can be used to claim priority from in later patent applications (to be filed directly in any country where protection is needed, or indirectly, via the PCT system) then you can even file a patent application without payment of any official fees. Such a filing can be achieved at the European Patent Office, and many of the national patent offices in European countries. Filing of such an application can be done by anyone.
However, for such a filing to be effective, i.e. to provide sufficient basis for a later priority claim, should still be as complete as possible and certainly should provide all information that a skilled person would need to repeat the invention (i.e. it should fulfill the enablement requirement). Since drafting of patent applications is difficult and should be done with the utmost care - also the drafting of such a 'provisional application'- it is strongly adviced to seek the help or advice of a patent agent or patent attorney.