What does it take from the airlines to be ETOPS certified?
The requirements for ETOPS certification by the FAA are outlined in the following Advisory Circular:


  ETOPS QUALIFICATIONS. The unique nature of ETOPS necessitates an evaluation of
  these operations to ensure that the certificate holder's proposed programs are effective. The FAA
  will review the certificate holder's documentation and training programs to validate that they are
  appropriate for ETOPS. To receive approval to conduct ETOPS the certificate holder must
  satisfy the following conditions:
  
  a. Airplane. The specified airplane-engine combination listed in the certificate holder's
  application must have been certificated to the airworthiness standards of transport category
  airplanes and must be approved for ETOPS. Guidance for airplane ETOPS type design can be
  found in AC 25.1535-1 and § 121.162.
  
  [...]
  
  b. Flight Operations and Maintenance Requirements. The certificate holder must show
  compliance with the flight operations requirements discussed in paragraph 303 and the
  maintenance requirements discussed in paragraph 301.
  
  c. Training Requirements. The certificate holder should show that it has trained its
  personnel to achieve competency in ETOPS and must show compliance with the flight
  operations and maintenance training requirements discussed in paragraphs 302 and 304.
  
  d. Requirements For ETOPS Approval. Before the FAA grants ETOPS operational
  approval to an applicant for two-engine ETOPS, the certificate holder must be able to
  demonstrate the ability to achieve and maintain the level of propulsion system reliability that is
  required for the ETOPS-approved airplane-engine combination to be used (appendix P to
  part 121, section I, paragraph (a)). The certificate holder must also demonstrate that it can
  operate the particular airframe and other airplane systems at levels of reliability appropriate for
  the intended operation. This can be achieved directly by a successful in-service operational
  history or by successfully validating all the required ETOPS processes according to the
  Accelerated ETOPS Application Method in Appendix 3 of this AC.
  
  e. Accelerated ETOPS Application. An applicant for an initial operating certificate who
  is applying for ETOPS authority at entry into service under the Accelerated ETOPS Application
  method must comply with the same requirements for certificate holders outlined in this AC. It
  should be understood that validation of an applicant with no previous operational experience
  should be more robust than would be necessary for a certificate holder with operational experience. As is the case for all Accelerated ETOPS approvals, the Director, Flight Standards
  Service must be satisfied that the applicant can operate to the standards expected of an
  experienced ETOPS operator from the first day of service.


(FAA AC-120-42B)

The referenced paragraphs 301 to 304 can be found in the same document and provide detailed requirements for operations, maintenance and training.

The details may vary around the world, but other aviation authorities will have similar requirements for certification.