You and your spouse fill out N400s. You get fingerprinted and interviewed. Then you take the oath. If your kids are under 18, have a green card and live with you, they become citizens the moment the first of you (i.e., you or your spouse) takes the oath. No fuss, no bother, no forms (see section 320 of the immigration act as amended in (I think) 2000).
At that point, you can get the kids US Passports with one of your certificates of naturalization (our kid was the first in the family to get a US Passport).
If you want, you can also fill out an N-600 for each kid to get them a certificate of naturalization. The passport process is quick (it's the Dept of State). The N-600 process is with the USCIS - so of course it is much slower (I'm not sure how slow yet, only 3 or 4 months have passed (we are expecting 6 months)). That gives your child a permanent record of his/her citizenship. But, even without the N-600, the citizenship exists from the moment the parent takes the oath.
HTH
