This will give you some info: https://www.ch.ch/en/family-reunification-eu-efta/
You may need to show your employment contract or payslips so they know you can afford to support them all once they move over. You'll need to pay for their permits, similar cost to yours I assume.
Now for the moving bit. Firstly, with 3 kids, depending on their ages, you'll need 3/4 bedrooms. Assuming that one is 8+ and the other two younger a few years younger then 3 bedrooms should do as the younger two can share. One for the parents, one for the older child and one for the youngsters to share. Of course if you want people to stay with you when visiting, then you'll need to look for 4 so as to have a spare bedroom for them when they come.
Secondly, if you're planning to move then I'd do that before bringing the family over providing you can arrange the move quickly. Why? Because you'll have to pay Geneva for their permits and then you'll have to do it all over again for the whole family when you change canton/commune so could get expensive.
This is where you need to go to register - don't forget to deregister from Geneva as well. http://www.nyon.ch/fr/officiel/servi...ants-776-30503
You'll need birth certificates for everyone and your marriage certificate - all less than 6 months old so you may need to order more copies.