The regulations don't specify the means of notification. If you do it by telephone you should make a note of the date time and the name of the person you notified. If by email, keep a copy of the email.
I'm not absolutely sure of the answer to your question about resigning to accept a job with another temp agency and then getting laid off. Resignations are not treated favorably under the unemployment statute. You would be okay if you resigned in order to accept permanent full-time employment with another employer, but I'm not sure about leaving one temp job to accept another temp job. You might be okay if you anticipated being laid off from the first job. The law on this kind of situation is complicated. In my experience many or most of the smaller agencies tend to contest anyone collecting UC against their accounts. I've never seen a case involving Kelly, Manpower, Robert Half or the big agencies, but I've seen plenty involving small temp agencies. And their testimony at hearings frequently isn't accurate, to put it politely.