To register for an ORCID, go to orcid.org and fill out a form, which will start out like the image below:
Note that they require that each person register for his or her own ORCID.
Open Researcher and Contributor ID (ORCID) is a not-for-profit organization, international in scope, which is developing a system of identification for scholars that as of this writing doesn't cost anything to register for and use. Therefore, the ORCID is more inclusive of a diverse and more international range of scholars, and is growing dramatically.
ORCID and the other identifiers have their pluses and minuses. Different organizations will prefer one or the other, or allow one or more to be used. Some grant providers or publishers require their grant requestors or authors to have a specific type of identifier. They are intended to help distinguish specific authors and associate them with their works.
ORCID identifiers start with the address of their web site: http://orcid.org/xxxx-xxxx-xxxx-xxxx, where the X's are replaced by a unique series of numbers.