Liaison librarians are expected to reach out to their specific departments and to collaborate with colleagues to develop innovative services in areas such as outreach, marketing, and digital resources. In terms of your own departmental outreach, librarians have considerable agency. Feel free to talk to your colleagues about what they do for outreach.
Who? You are responsible for reaching out to your assigned liaison departments as you see fit.
What? What information you choose to send is also up to you. Common information includes new resources, a reminder about information literacy, and the sharing of new services, such as reserves. You might want to keep track of the library's publication, The Academic Gateway, to avoid duplications. https://library.sjsu.edu/about/newsletters
Where? You will have a transition period during which another librarian is handing a department to you. When that happens, ask the librarian what contact has worked best. Sometimes, a librarian reaches out to the entire department faculty via a mailing list, others by hand-selected email addresses from the department's website. Occasionally, department chairs may prefer that you send outreach messages to them, or their office analyst, and they will in turn forward it to their faculty.
When? This is up to you! It's common to send outreach notices before or after a semester, or both. Choose the schedule that you find works best.