Once you have initiated the domain transfer the current and the new registrar will send you an email to the administrative contact email address listed in the domain.
(Note if the current administrative contact email in the domain whois database is not correct or is outdated and you already initiated the transfer, you will have to request the transfer process cancellation, then update your email address at the current registrar and request us to re-initiate the domain transfer.)
You have to approve the transfer to complete the domain registration transfer to the new registrar. This is done clicking in the approve link you will receive in the email sent by the new registrar as we said above.
Note if you do not take action (approve or reject the transfer) the transfer process will FAIL automatically after 5 business days.
Please also check in this KnowledgeBase the requirements to transfer a domain.