Whichever school they/their parent's choose. Some bases have schools and some don't. You can choose to go to school on or off base. If you live off base, it's pretty much the same as being a civilian, wherever is closer to where you live.
Many military installations offer schools on post and historically Department of Defense schools rank higher than public schools. However, not all soldiers live on post and dependent children can also attend the public schools in their local community.
On base if there is a base school and they are in the district. Most likely they just go to the public school for their neighborhood. The exception is when we are overseas our kids go to DODDS overseas schools. A lot of military families are homeschooling because we move so often and it is difficult for the kids to change schools so much.