In large part, this is going to depend upon the rules in your office and the laws in your area.
In the United States, the Family Medical Leave Act, or FMLA, could potentially be in play here. In the State of Washington, the Washington Family Care Act imposes additional rules when it comes to sick leave.
Unless you are say going to be out for an extended period of time, because of either a planned or unplanned major medical issue, it's generally accepted most places to call in each and every day you are out sick. If it were me, I would have called in sick each and every day that I was out sick.
The means of notification will also vary from one organization and supervisor to the next. Some will insist upon a live human being speaking to another live human being over the phone. Others are fine with voice mail or Email notifications.
Increasingly, I see Email notifications as superior as I routinely see instances of people calling in sick, getting voice mail, and the person who gets the voice mail is themselves out of the office--either for sick or other purposes. I personally send an Email to the Team Email Distribution List, which includes both my supervisor and my coworkers. In my view, this provides for the greatest possibility of someone who needs to get hold of me getting the message that I won't be in the office that day.
As for what to say, as a Union Shop Steward I tell people to be brief and not go into details. This is especially true with FMLA, but it is serves everyone best if the information is brief. "I am out sick today." "My child is sick today." "My elderly parent is sick today."