The breeding process in Pokemon Sword and Shield is a fairly straightforward process that helps you build your team of Pokemon to fight.
It all comes down to this: you leave two Pokémon of opposite sexes and the same group of eggs in a Pokémon nursery, and after a while they will make an egg. It is important that they are in the same group of eggs, otherwise they will not breed together. You can see the different egg groups here in Serebii's list.
The only exception to this is Ditto. Other than Mythical and Legendary Pokémon, you can breed any Pokémon with a Ditto. You can find these chameleons in the Outrage Lake area.
Pokemon breeding
Once you have the Ditto or two Pokémon in hand, you'll want to head to a Pokémon Nursery, which is in the Bridge Field area and on Route 5.
Image via PolygonTalk to the nursery worker outside and you can give him the two Pokémon you want to breed. It's going to take a little while for the magic to happen, so explore the area or go take care of other things you want.
Check back with the worker regularly and when she has her arms raised in a thinking posture, it means the egg is ready.
Speaking with the worker, she'll tell you how compatible the two Pokémon are, or if they don't get along as well. Don't worry if it is the latter; they will always happen again, it will just take a little longer.
How to boost your breeding
There are several things you can do to boost your breeding:
After taking out Leon in the Pokemon League, you can then take on Game Freak designer Shigeki Morimoto at the Ionia Hotel in Circhester. If you beat it, you'll get an Oval Charm, an item that will increase the amount of eggs Pokémon will produce.
You may also wish the nature of your parent Pokémon to be passed down to the offspring, in which case you can give an Everstone Stone to the parent Pokémon. This will ensure that nature will be transmitted as long as it is the same species.
In order for your eggs to hatch faster once you get them from the Nursery, you can carry a Pokémon with the Flame Body ability. The Pokémon that all have a chance for this ability are Sizzlipede, Centiskorch, Carkol, Coalossal, Litwick, Lampent, and Chandelure.
Finally, some Pokémon will need to contain a certain item in order to raise a specific baby Pokémon. Here is the list of them: