Summarize this article:

Once the birds have mated and the eggs are fertilized, the female will begin laying eggs in about 10 days. She will lay 1 egg at a time, so you'll see a single egg appear in the nesting box. Sometimes budgies need to breed several times before the female’s eggs are fertilized. After the female lays her first egg, there will be a 1-2 day gap between each egg in her clutch. She will continue to lay an egg every day or 2 until they are all laid. In captivity, she’ll likely lay 4-8 eggs in total. She will lay her eggs in the nesting box. Your female bird won’t start incubating the eggs until she’s laid at least 2 or 3. That means you’ll likely see 1 or 2 eggs sitting neglected in the nest after she’s first started laying. This is normal, so don’t worry if your bird is not being attentive in those first few days. The female budgie will always be the one to sit on the eggs. The male shouldn’t go into the nesting box. When they start to hatch, you’ll notice cracks appearing on the egg shells. It may take awhile for the budgies to hatch, but don’t help them. If they’re healthy, they’ll emerge from their shells after a few hours. If you have eggs that haven’t hatched after 22 days, it’s best to throw them out. They likely won’t hatch. If they do, the babies won’t be healthy. Budgies generally take good care of their young, but keep an eye on the little family to make sure none of the babies are being neglected. If there are several babies, the mother may neglect the littlest chicks. You may want to hand raise baby budgies that are being neglected.

Summary:
Wait 10 days after a successful breeding for the first egg. Expect your female budgie to lay 4-8 eggs over about 2 weeks. Make sure your budgie sits on the eggs after the 3rd one is laid. Watch for hatching after 18-21 days of incubation. Make sure the mother is caring for her baby budgies.