My NCBI is a user account within PubMed that allows you to save citations and searches, set unique search preferences, and set up search alerts, and have other advanced options within PubMed. Anyone can register for My NCBI with an email address and password.
Begin by simply clicking the "Log In" link in the top right corner of the PubMed screen:
This is a short video which describes how to set up a My NCBI account and use it to save searches.