In order to transfer a domain name from one registrar to another you would need to follow the transfer procedures of the gaining registrar (the registrar the you are transferring to).
You should be required by the gaining registrar to verify the request to ensure it's legitimacy. Once the transfer request has been verified, the gaining registrar will submit the transfer request to Verisign Global Registry. Once a transfer request has been submitted to Verisign, the current registrar for the name will receive notification of the request. The Global Registry will allow the current registrar up to 5 business days in which to approve or decline the transfer request. You may or may not receive verification material from the current registrar.
Each registrar has their own policies concerning transfers away to another registrar. It is a good idea to contact your current registrar in order to make yourself familiar with their policies in order to avoid potential delays. Some registrars have names locked against transfers that must be removed before a request can be submitted and some may send a verification email to verify the transfer away.