1) soak the oats for as long as you like (I do overnight, but can be as little as 30 mins)
2) Pass through a sieve, removing the sitting liquid.
3) Add to a blender with some fresh water and pulse (the amount of fresh water depends on how thick you want it to be afterwards). You can also add cocoa powder here if you want oaty/chocolatey milk.
4) Pass the liquor through a nut milk bag (or muslin etc...) to get the milk.
It separates quite easily so you do need to shake before use, but should be easily achievable with household items.
(Not OP) Oatly's process is patented, so you can look up what they do. That places some restrictions on using it in the same markets, of course. I think it's this one:
Recently tried making my own and it's a really nice process to go through (to the extent am looking at small scale manufacture).
If you can, definitely try it in a flat white back to back with cow's milk.