The Content-Type header of requests and responses is defined by the consumes and produces keywords, respectively. They can be specified on the operation level or on the root level of the spec.
The Authorization header is defined using the securityDefinitions and security keywords. OpenAPI/Swagger 2.0 supports Basic authentication, API keys and OAuth 2.
Other headers can be defined as in: header parameters.
For example, if an operation POSTs JSON and uses Basic auth, you can describe it as follows:
swagger: '2.0'
...
securityDefinitions:   # Authorization, part 1
  basicAuth:
    type: basic
paths:
  /something:
    post:
      summary: POST some JSON
      consumes:
        - application/json  # Request Content-Type
      produces:
        - application/json  # Response Content-Type
      security:
        - basicAuth: []     # Authorization, part 2
      parameters:
        - in: body
          name: body
          required: true
          schema:
            $ref: '#/definitions/Something'
      responses:
        200:
          description: OK
Relevant documentation:
MIME Types
Authentication
Describing Parameters