Although I don't know as much about the crusades as I would like, this question does periodically come up on this subreddit and always underestimates the amount of international trade going on in the pre-modern world, especially in the Mediterranean. Although our modern "Merchant Adventurers" like business executives, entrepreneurs, and international salespeople travel on airliners, hire trained translators, and if need be just ask Google, this doesn't mean that multilingual and multicultural people are a recent invention. The Mediterranean cities were major centers of commerce and trade, some were even more multicultural in the past than they are now!

Now, although no Crusader specifically wrote, "We found this guy who spoke Greek in Marseilles and took him with us," (and if one did, it certainly didn't trickle down to us as far as I know) just to give in example, many Italian mariners in Venice, major middleman in the whole process of Crusading, were fluent speakers of Greek. Indeed, a large proportion of the residents of Venice could be expected to be multilingual: many sailors were Italo-Dalmatians who had either learned the Venetian dialect as a second language growing up in the Venetian-controlled cities in Dalmatia, or quickly picked up the language working on Venetian ships. Until 1405, when the Venetians came to control a neighboring city on the mainland called Padua, upper-class Venetians were often sent to Constantinople to complete their studies (and Norwich, in his History of Venice even affirms that many a Byzantine sent his daughter across the Adriatic to marry a Venetian).

Upper-class Greeks in the Byzantine empire, on the other hand, could very well be expected to have studied Latin. Their pronunciation might have been a bit off, but there is no indication they wouldn't be able to communicate with the better-educated crusaders also well-versed in Latin. In fact, in the first three crusades there are many more records of Venetians being contracted to haul crusaders off to Greece or the Holy Land than there are records of Venetians doing much else, clear indication that the Frankish crusaders weren't desperate for the Greek-speaking Italians to render their services much more than needed.

Venetians who operated the trade routes from Alexandria could also be expected to have some fluency in Arabic (although I'm not too sure what language would be the dominant one used by Northern Egyptian port authorities and the mercantile community at the time of the first crusades). The Venetians, and merchants in other Italian cities, had operated these trade routes for generations (hundreds of years, in fact) and older merchants passed on their knowledge and language skills to younger ones. There were also Greeks working on Italian ships as well as operating their own trade routes in the eastern mediterranean, and these people would also have working knowledge of multiple languages; it wold not be difficult for the Byzantines to set up an interlocutor, in fact they probably already had several people who could do the job either at the Imperial court or within the imperial administration, many of whom had studied languages as part of their education.

Lastly, the inhabitants of the Holy Land themselves could be expected to be fluent in multiple languages. No one region of the world exists in a vacuum, and it is almost certain that at lease some people living in the Levant must have known how to speak Latin, Greek, and Arabic even prior to the Arab conquest.

A good history of an Italian Merchant Republic that gives an idea of the extent at which trade routes crisscrossed the mediterranean is the aforementioned History of Venice by John Julius Norwich. Norwich also wrote an extensive history of the Kingdom of Sicily, which might also be interesting lens to understand what ethnic dynamics could look like in a pre-modern state (although granted, the Sicily was a particularly unique case). I actually breifly wrote about it as part of a longer thread you can read.