You first need a completed nest that a blue jay has helped build. (If you don't have one, you'll need to get a nesting tree and build one. It takes 5 different types of birds to complete a nest and each multiple of 5 will contribute.)
Once you have the nest, place it in your garden. The next multiple of 10 blue jays will nest once spotted. Then, click on the nesting bird to receive your task. (You'll have to spot anywhere from 1-5 of a specific kind of bird.)
When you complete the task, the nesting bird will lay an egg. Then, just leave out bird mix on a low table so it can hatch.
(If you want to try for twins, your best chance is to put out two low plates of birdmix at the same time and hope the chick comes to both plates.)
You can look at this thread to see how to self-gift a nesting tree, if you need one:
https://www.fairylandgame.com/fbfairy/forums.php?tid=134704 Additionally, you can find more details about building nests and getting chicks here:
https://www.fairylandgame.com/fbfairy/forums.php?tid=34384