When you take a decision to book anything, make sure you have all the "bits of paper". That means the passport if you're flying internationally. The rules about passports for children are in a state of flux as the new biometric or e-passports come into use. The original system used to add children to their parent's passports but, increasingly, countries are requiring children to carry their own passports with data in machine readable form.
There are also different rules about how often to update the photographs to keep pace with changes in appearance as your children age. Because the air companies are fined if they bring people to a country without the right documents, you can expect to be turned away at the airport if your documents are not in order. So check the destination countries to see what is required to enter their territory, and check your own government to see what is required to come back home. The fear of terrorism has forced many changes and you need to be up-to-date. Flying domestically, you may need proof of the children's ages and, if one parent is traveling alone, it can be a good idea to carry a letter of authority from the other parent. There are many cases of child abduction and, when you are crossing state lines, many airlines are now asking for proof that the journey is approved by the other parent. It may also be appropriate to carry a power of attorney authorising the sole parent to give consent on behalf of the children should medical treatment become necessary.
With all the paperwork done and the tickets bought, you now need to plan your flight. How much are you allowed to carry on board? Now work out what you need for the children. Making allowances for the rules about taking liquids on board, find out whether you can take bottled water or sodas and snacks. What meals will be served on board, and will they be suitable for your children? How are you going to keep them entertained? The problem rises more and more as the flight becomes longer. You will need diapers for the young and possibly a change of clothing for older children just in case they vomit over everything. Think of all the worst case scenarios and take what you can within the weight limit.
Then it is off to the airport and a date with destiny. Family holidays are great fun once you arrive. One final thought - some budget airlines with cheap plane tickets have hidden charges if you do not check in online. Some also charge for transport within the airport to get from the terminal to the plane. The fact that the plane tickets may be cheap gives the airlines an incentive to find other things to charge for. Make sure you have read all the small print and carry enough cash or credit cards to pay as you go. That said, cheap plane tickets may not give the best experience, but they are the means to get you to the end destination and a good holiday.