Apologize and tell the other person that you completely forgot about the appointment. Honesty is always the best policy. Don't lie and blame your kids, pets, car, etc. People will wonder if you're really telling the truth. Still, if it was a family issue, say so.
Many clients respect people who put family first.
Call as soon as you realize that you have missed the appointment. A verbal apology is better than no apology at all. Ask to reschedule another meeting as soon as possible. Be accommodating and offer to inconvenience yourself to make it more convenient for the client. If you know you're going to be late for an appointment, give the other person a courtesy call to let them know how late you'll be.