First it has to have a mate. And then they prepare a nest to lay their eggs in. By shredding paper and gathering things to make a nest. If there is nothing and its their time they will lay an on the the bottom of cage.
First, you must have a male and female (of course, lol) and should notice some extra-friendly behavior between the two (you may not see them breeding, some birds are particular about that, but you might witness them feeding and preening eachother a lot and constantly around one another, or the male putting a foot on the female’s back whenever he gets a chance…which indicates he is trying to breed her). Your female will start to look a little chubby around her lower abdomen (not all birds will, if she is naturally large, or overweight, you might not notice it, but if she is usually slim, it should be visable). She will be moodier, and probably antsy if you don’t have a nesting box in there for her with proper bedding. The male might become more protective of her, and overall a little more agressive because of the anxiety she is expressing. She will start dropping large, wet stools when she comes close to laying (at least, that is what my female did, and only when she was close to laying). She will also need more calcium in her diet to ensure safe laying and healthy eggs. Be sure to supply her with cuttlebone, and/or a mineral block and perhaps supplement their feed with sprouts and/or fruits and veggies (just not avocado; this is toxic to budgies).
If you don’t have a box, and she seems to be getting a slight larger, or you’ve witnessed your birds breeding, or the male attempting to breed and you are up for the challenge, provide your female with an appropriate nest box which you should be able to buy at your local pet shop/bird farm. Just specify that it is for a budgie pair and you’ll be fine. Get some bedding for it as well, and layer it a good two inches or so thick on the bottom. Your female should instinctively check it out soon enough after it’s introduced and start to build her nest. If she is “pregnant”, she’ll lay her eggs every other day, and the father should take note to feed her, etc. She won’t come out much, other than to feed, drink, poop, and relax a little. Most of her time however will be spent with her box and eggs.
Ask your local pet shop/bird farm and do some research on the internet on breeding information on parakeets. Pick up a book on the birds that has a chapter on breeding. This should help you get a more conclusive and outlined idea of how to care for your pair’s and their future offspring’s needs