I don't really know much about the process but I would imagine it is probably different depending on which top level domain you are talking about, the process for .ie would likely be different than for .com (for instance it is more difficult to register .ie so the new owner would also likely have to satisfy the criteria whereas nearly anyone can register .com). It therefore might help if you specify which type of domain you mean.
If you are the registered owner, then the site that you registered with should offer a facility to transfer the ownership to another person.
for example offers this facility - not sure if this is only offered if you registered the site with them, but perhaps not, as domain registration is a regulated thing so there are defined rules and regulations governing this.
On GoDaddy, you enter the email address of the person you wish to transfer the domain to and GoDaddy then send them an email for them to register a new GoDaddy account and complete the registration.