It isn't unusual for well-traveled people to learn a dozen languages fluently enough to do business - and perhaps more, if some of the languages are closely related, such as German, Dutch and the Nordic languages. The TNG "Icarus Factor" reference to a man who spoke forty languages (supposedly beyond "hello" and "thank you") would still count as a freak show level achievement today, though.
One wonders whether space aliens could have languages that are so radically different from Earth ones that they pose a special difficulty in learning. After all, many Earth languages are pretty dissimilar from each other already. If the aliens speak in the classic human manner, that is, use vibrations of air to communicate their thoughts and do not add a significant degree of body language or other complications, then learning their languages probably wouldn't be more difficult than learning human languages.
I mean, yeah, there's a lot of common ancient heritage to Earth languages. But I for one come from a country where the two most prominent languages are utterly unrelated to each other in terms of deep underlying grammatic concepts - even if both languages have later been encrusted with common "international" vocabulary. I really cannot fathom how Klingonese or Cylonese or Coruscantian could be more distant from my native Finnish than my also-native Swedish is...
Timo Saloniemi