They may or not speak their own language. That's what Universal Translators are for.
The official language of the Federation is Federation Standard, which the viewer percieves as english because of the omnipresent universal translator. However with the universal translator, member races can continue to speak their native languages.
Kind of like Esperanto?
A language that has 47 different words for "photon torpedo".
"Federation Standard" has never been mentioned in canon.
The universal translator is developed enough that a person should be able to communicate in his or her native language wherever he or she goes. As far as reading and writing, nearly every LCARS display we've seen on screen has been in English, and on at least one occasion, the language was positively identified as English. This would lead me to assume one of three possibilities:
- 1) English is the major working language of the Federation, or one of the major working languages, along with Vulcan, Andorian, and a few others. Starfleet members on ships with human-majority crews can read and write English.
- 2) The universal translator works for printed material as well. This idea has never been mentioned in canon, but it's possible.
- 3) LCARS changes its language depending on whoever is viewing it at the time.
I would say a combination of 2 and 3 is probably the most likely, as there have been numerous examples of Starfleet members operating alien computer systems with no trouble, as well as aliens operating Federation computers. English is probably the "default" language on Starfleet vessels with human-majority crews. Ships with Vulcan-majority crews have also been mentioned, Vulcan is likely their default language.