What is the procedure to turn a certified aircraft into an experimental aircraft?
You essentially convert it to Experimental Exhibition, not Experimental Amateur-Built. That means more restrictions, depending on the FSDO. For instance, your operating limitations may prohibit passengers, or require permission for every flight over a given distance.

It is said that the FAA can be sensitive to people trying to put type-certificated aircraft into Experimental category for recreational use. Important advice below is that you should get permission from the FSDO before starting work on the airplane.

Even if you do this (and they likely won't like you converting say a Cherokee or a Cessna 172 to experimental), they will place certain restrictions on use, such as only flying within a 25 mile radius, and every year you may have to submit a "Program Letter" with a list of all the fly-ins and shows you are going to go to (since it is experimental-exhibition category, so you need to exhibit it!)

All that is to say, you probably will have a hard time converting a certificated plane to experimental and using it like it seems you intend to from your question.

Here is the relevant section from FAA Order 8130.2H.


  Section 10. Certification and Operation of Aircraft Under the
  Experimental Purpose of Exhibition or Air Racing
  
  
  General. Under the provisions of § 21.191(d), exhibition aircraft are defined as aircraft that exhibit the aircraft’s flight
  capabilities, performance, or unusual characteristics at air shows,
  fly-ins, and aviation events; for motion picture, television, and
  similar productions; and for the maintenance of exhibition flight
  proficiency, including (for persons exhibiting aircraft) flying to and
  from such events and productions. Under the provisions of § 21.191(e),
  air racing aircraft are defined as aircraft that participate in air
  races, including (for such participants) practicing for such air races
  and flying to and from racing events. 
  
  
  a. Exhibition. A certificate for
  experimental exhibition must only be issued when an aircraft is to be
  used for valid exhibition purposes. Included in those purposes are
  organized air shows, organized fly-in activities, organized
  exhibitions, youth education events, organized aerobatic competition,
  fly-ins or meets, and movie or television productions. The duration of
  an airworthiness certificate for exhibition may be unlimited.


Here is an example of how to do it I found on a old page from the Robinson V8 Seabee Company website. (I found the page in the internet cache, so it is likely this method isn't foolproof)

STEP 1

Submit bill of sale for project Aircraft as "bought for salvage Parts" to the FAA. Add a separate letter of salvage in order to remove it from the FAA registry as Salvaged. This de-registers this A/C and is an important first step.

STEP 2

Obtain written permission from your local FAA Flight Standards District Office (FSDO) inspector in order to remove the data tag from the salvaged project aircraft. This step represents a great opportunity to develop a positive relationship with the FSDO inspector with whom you'll be working to complete the process. Be straightforward and explain that you require his help in order to certify your project in accordance with 14 CFR § 21.193, under a Special Airworthiness Certificate for the purposes of operating an aircraft in the experimental exhibition group 2 - Piston Engine Aircraft category, for the purposes of: 


  Demonstrating flight proficiency; Demonstrating the superior engine
  reliability of modern V8 engines; and  Participating in exhibition of
  the aircraft at airshows and public event in order to educate the
  public about the unique and interesting characteristics of this
  aircraft


It is important to understand that the FAA FSDO inspectors are busy folks, and that they will appreciate the fact that you've done your homework. Maintain professionalism and don't expect an answer on the spot, as these inspectors have a number of strict procedures and guidelines within which they must work to accomplish the goal of certifying your aircraft. They deal with a great variety of aircraft and requests and may require some time to get up to speed on your specific request and understand the nature of your Robinson V8 aircraft.

STEP 3

Reserve a new N number on the FAA web site.

When your new N-number is confirmed  by the FAA, simply submit forms 8050-88 and 8050-1 for the new N number as:


  Manufacturer (preferably your new LLC Company or yourself). It cannot
  be the old manufacturer of the salvaged parts. Model  (Example:
  Military Seabee OA-15) or whatever you want to call it.  It cannot be
  the old model of the salvaged parts.


These forms need to be sent to the FAA Oklahoma City Registration Branch.

When your project is completed and ready for airworthiness inspection and operating limitations, issue a program letter to your FSDO inspector.  With FAA application for airworthiness form 8130.6.  They will take it from there.

Here is an example of program letter:


  Program Letter Nxxxx
  
  Date:  May xx, 20xx
  
  To:  Mr. FAA Inspector
  
  Federal Aviation Administration
  
  XXXXX Flight Standards District Office
  
  1234 Maple Lane
  
  anytown, state zipcode
  
  In accordance with 14 CFR § 21.193,  I request a Special Airworthiness
  Certificate for my aircraft Nxxxx for the purpose of operating an
  experimental exhibition, group 2 -  Piston Engine Aircraft. 1) For
  purposes of demonstrating flight proficency.  2) To demonstrate the
  superior engine reliability of modern V8 Engines.  3) To participate
  in exhibition of the aircraft at airshows and public events to educate
  the public about the unique and interesting characteristics of this
  aircraft.
  
  The aircraft description is as follows:
  
  Manufacturer: Your LLC                                    Registration
  No.:    Nxxxx
  
  Model:  Your model
  Serial No.:    xxxxx       Engine Make/Model: Robinson  LSV
  No. of Engines:    01 Propeller Make/Model:    xxxxx
  
  Number of Seats: Four
  
  The aircraft will be available for inspection at it’s base airport:
  (your airport and hangar location).
  
  The aircraft will be weighed prior to flight to determine weight and
  balance data. The marking requirements of Part 45 will be complied
  with prior to flight, including permanent attachment of a fireproof
  identification (data) plate, permanent application of appropriate
  registration marks.
  
  The following placards will be displayed in the cockpit in full view
  of all occupants:
  
  The word “EXPERIMENTAL" displayed near the entrance to the cabin or
  cockpit; minimum 2 inches, maximum 6 inches in height.
  
  "Passenger Warning – This Aircraft Does Not Comply With Federal Safety
  Regulations For Standard Aircraft" .
  
  Instruments and system controls will be adequately marked, identified,
  and function properly prior to flight.
  
  The power plant /propeller will be ground-run to sufficiently
  determine they are operating properly for flight.
  
  The Aircraft will be maintained under an Annual condition inspection
  that meets the scope and detail of 14CFR part 43, Appendix D.
  
  I request that airworthiness certification operating limitations be
  issued permitting me to operate the aircraft in phase one within 50
  Nautical mile radius of (Your Base Airport) with the exception of all
  A,B,C and restricted airspace and avoiding flight over populated
  areas.  Ten hours of  phase one flight tests will  be conducted to
  demonstrate control ability, engine reliability and establish the
  flight envelope.   After Phase 1 flight test completion,  I plan to
  operate the aircraft under Phase two operating limitations under
  VFR/day and VFR/night conditions under a group 2 Experimental
  Exhibition airworthiness certification within the continental U.S.
  proficiency area.
  
  Kind Regards,
  
  You