How will you know if you are truly prepared for a nuclear event? Practice. Schools, businesses, and families have fire drills and tornado/hurricane drills, so why not have a nuclear drill?
Once the basics of your fallout shelter are laid out, (who's sleeping where, at least a few weeks worth of supplies are stored, etc.) you are ready for the drill. If you are serious about preparing, then you probably keep tabs on the news. You know when tensions are high between nuclear armed countries. This will give you a heads up: you can double check that supplies are in date, buy a few extra supplies (don't go broke buying supplies in case there is no nuclear event), and you can move some extra things into the fallout shelter. I have a small generator that is portable and solar powered. If a nuclear event seemed likely, I would move this into my fallout shelter in a metal trash can to try to protect it from EMP. I would also put my laptop, all rechargeable batteries and charges, and any other small electrical devices I might need later. I would also move may dogs, cats, and chickens into their cages in the fallout shelter. All of this will make going to the fallout shelter, whether a drill or not, easier and less stressful for everyone.
Everyone should have a bag filled with extra clothes and an extra pair of shoes (if you have kids, make sure the clothes and shoes are a size or two too big, so they won't outgrow the clothes before they can use them). Once a drill is called, everyone should grab their bags and anything else they are responsible for taking to the shelter (older children and adults can take the rest of the guns and ammo, younger children can take a small bag filled with snacks or entertainment, for example). Some drills may only be about getting to the shelter, while others should be about living in the shelter. From time to time, spend a day or two in the shelter doing everything like you would if there had been a nuclear incident. It is important you do everything like you would if you have to stay inside the shelter. Use the bathroom, bathe, cook meals, entertain yourselves, be on guard, everything just like you would have to do during a real event. Also, make sure everyone practices light and noise conservation. During a real event, you wouldn't want the wrong people to know you survived because they heard you laughing or saw some light coming through the window.
Don't scare your kids, but make sure they understand how important it is. Kids are taught how important fire drills and tornado/hurricane drills are, so teach them how important nuke drills are. Have a plan for picking them up from school if it looked like an event was about to happen, and tell them your plan so they won't worry. Make sure you kids know that you will always do your very best to keep them safe.