Decide who will be driving. If financially possible, rent a car and driver or join a tour group for the day (check in advance to see that kids are allowed). If not, designate a driver who will not be sampling wine so everyone has a safe trip. Napa wineries are fairly spread out, and walking between them is not a practical idea.
Pick a winery your entire family can enjoy. You don't want to head to the small winery with a tasting room and no tour when you have children. Check out the wineries that are more family friendly. For example, Sterling Vineyards has a tram that takes you from its parking lot high in the sky over the Napa Valley. It's like going on an amusement ride as far as children are concerned.
Check on what's available to drink. While the adults are tasting brightly colored and fruit-fragrant wine, most children are not going to be happy with a cup of water. Question the wineries beforehand to see whether they offer anything other than water for those not drinking wine. Castello Di Amorosa, which houses its winery in a 13th century castle, is one of the wineries that provide kids with grape juice.
Pack some fun for your children, unless you are sure that they will be well-occupied. At Frogs Leap Winery, kids have an opportunity to explore its vegetable garden, barn and fruit trees while the parents are learning about wine. Many Napa Valley wineries also provide coloring books and crayons for children. Just to be sure your kids are occupied, bring along a few toys for them to play with or books that they can read.
Teach your children about wine-making before you go so they will look forward to touring the wineries. Wherever you can, show them the grapes on the vines so they can get a good idea about where it all starts. Most of all, don't forget the camera because you will want memories of the outing.