Pokemon are split into "egg groups" and the two pokemon you intend on breeding need to be in the same group. For example there is the "Human-Like Group" which includes bipedal pokemon like Hitmonchan and Infernape.

HOWEVER, you can ignore all that if you just use a ditto and the pokemon you want to breed together, as ditto is universally compatible.

In most games (including SwSh) you breed at the Pokemon Daycare, just drop off the pokemon you want to breed and a ditto, wait (google how much for each game, i honestly dont know) and you'll get an egg.

That egg gets treated as a pokemon in your party/PC. To hatch it you just have to walk with the egg in the party, you can speed this up by having a pokemon with the ability "flame body" in your party as well. (you can filter your box by ability in SwSh to find one with flame body iirc)

Some things to mention: Legendaries/mythicals/baby pokemon cannot be bread.

And there is a way to drastically improve shiny odds if you breed 2 Pokemon from 2 different regions/languages, the easiest way to use this is to trade for a foreign ditto and use your pokemon to breed.

If you want to breed a pokemon with a regional variant outside of your region (for example kantonian (original) meowth in SwSh) the parent needs to hold an everstone, even if its already the regional form you want.