Here are some relevant passages from ISKCON Law regarding the initiation procedure.
2.3. First, or Hari-Nama, Initiation
2.3.1. Qualifications for First Initiation
126.96.36.199. One year preparatory period
In order to receive first initiation one must have been engaged favourably in devotional service, strictly following the four regulative principles and chanting sixteen rounds a day, for at least one year without interruption.
188.8.131.52.1. First six-month period
During the first six months of following the four regulative principles and chanting sixteen rounds daily, a new devotee who is aspiring for initiation should not commit himself to a particular initiating guru. Rather, he should chant Srila Prabhupada's pranama mantra and worship him as Founder-Acarya of ISKCON and as his siksa guru.
184.108.40.206.2. Second six-month period
After successfully completing the first six-month preparatory period, and after passing the required examination, the candidate may choose his future diksa guru. Receiving permission from that guru, and notifying the local temple president, the candidate should take shelter and begin to worship that guru as his own spiritual master and chant his pranama mantra. Actual initiation may take place only after a minimum six-month period from the date shelter was taken and the local temple president notified.
220.127.116.11.3. Devotees residing within temple communities
In addition to satisfying the above requirements, devotees residing in temple communities must, during the one-year preparatory period, regularly attend the full morning program.
18.104.22.168.4. Devotees residing outside temple communities
Devotees who do not live in a temple community and who cannot come daily to the temple programs may be initiated provided they have regular morning programs at home or attend regular morning programs at the Nama hatta centre.
22.214.171.124. Pass examination
Before a devotee can be permitted to formally take shelter of a particular ISKCON spiritual master and be subsequently recommended for initiation, he or she must demonstrate a basic understanding of Srila Prabhupada's teachings by answering an oral or written test administered by the temple president or other recommending authority. The questions to be answered are: see below.
2.4. Second, or Brahminical, Initiation
2.4.1. Qualification for Second Initiation
126.96.36.199. One-year wait between first and second initiation
To be qualified to receive second initiation, a first- devotee must have been steadily engaged in favourable devotional service, chanting sixteen rounds a day without fail, and strictly following the four regulative principles for a period of at least one year from the time of receiving first initiation. In addition, the candidate must have regularly attended a morning program, whether in a temple, preaching centre, nama-hatta centre, or at home.