You need to capture enough (number varies based on your current game parameters) cities with C.L. (LOCAL) buildings of that other continental culture, then you get C.Ad. (ADOPTED) of it in your capital and can build C.L.s of it yourself in your other (connected) cities.
It's not that intuitive for games where you need to capture several C.L.s, I admit.
If anything, I wait until I can literally see inside the enemy cities (via enough Espionage), so that I'm sure they have a C.L. built already (it's not a very high priority for AI).
Otherwise, you can literally capture the entire world and NOT get a single new continental culture, because AI simply wasn't building C.L.s yet, lol.
You can also get a free automatic European culture specifically by building Ellis Island, but it's so far into the future that it kinda almost doesn't count.