How do I prepare for a half marathon? 38yo mom of 4!

Training guide. Learning some of the basics will help you get started and to achieve your goals. Education, motivation and the right gear, this should be a good starting point for anyone who wants to hit the roads.
Planning. You are probably excellent at planning as a mother of 4. There are some excellent books out there with varied training plans. Runner's world Marathon/Half Marathon is one. Also there are some about training only 3 days per week for a full marathon. Check out running store for recommendations and contact running club locally. Take enough time to prepare - 16 weeks is reasonable. Good Luck !