You'll need to submit a request to your registrar to either update the 'whois' contact information or start a transfer process. Once a transfer is started, an email is sent from the registrar to the email address registered to the administrator contact of the domain name (current owner). They will need to reply from that same email address to verify that it's OK to make the transfer.
If you transfer ownership there may be a transfer fee involved. It is usually cheaper to take over ownership from another person, change the password, then update the registrant name, billing address, technical contact, etc.