In Man of Steel, when General Zod & company arrived to Earth, they broadcast a message in many Earth languages. We've also seen them speaking English.
How do they know Earth languages?
The Kryptonians have had space travel and advanced technologies for 100,000 years. Consider in all of that time in space they surely have come across other species and utilized translation technology allowing them to broadcast in multiple languages simultaneously. Their ability to send data to multiple locations should have been little more than a party trick.
As far as their ability to speak English, we are not told how long they hovered above the Earth before they decided to tell Humanity to turn over Kal-El. They could have simply learned the language before arriving.
Canon precedents indicates Kal-El was capable of speaking every Earth language and able to learn languages extremely quickly. So having the intellectual capacity for language isn't beyond the scope of Kryptonian abilities, at least from a canon perspective.
They have ridiculously advanced technology, so they could have just listened in on our broadcasts for a little while and figured out the languages that way. Furthermore, we know that they aren't exclusively soldiers
since one of them was going to dissect Superman to retrieve the Codex,
so it's conceivable that they had a space-linguist on board.
A better question would be 'why are they all speaking fluent English', but that could also be answered with 'alien technology' in the form of some kind of real-time translation device.
Two words: highly advanced technology and omnilingualism under a yellow star. This time was highly advanced technology, and surely they learned the language before arriving at Earth.
Though Kryptonians can learn omnilingualism, and speak or understand any language they come into contact with, this power has not yet been shown in the Man of Steel universe.
None of these really answer why they spoke it on Krypton also. Since a lot of other worldly figures in comics speak english, I like to think they all adopted the easiest language in the universe so that they could better communicate with others and Earth hasn't got the memo lol. But this is all just my imagination.