Did you already need to know Latin? If so, how much? Did you need to have read anything in particular, or to be able to answer any theological questions?
Nope. As long as you were a catholic and not in conflict with the church, you could join, and you'd be taught what you need. There are numerous accounts of people just showing up at the monastery and becoming monks in medieval sources.
So, why didn't all the homeless or poor do it? Well, look at the rule of monastic orders, and you'll see why. The monk's life is a life of hard labor and no fun at all, no possessions, no sex, work all day, pray all night.
That said, there are two exceptions:
Some orders had stronger conditions for joining, most prominently warrior monks, the big three being Templar, Teutonic and Hospitaller. To join Teutonic order, for example, you had to be a noble in the first place, and had to speak german (this was later changed to just nobles of Holy Roman Empire).
There's a loop hole in every rule I saw that you had to have vocation. What this means in practice: the decision to accept you or not ultimately rested on the abbot of the monastery, who could just send you packing if he had a bad day. Not an exam by any means, though, they weren't really a thing in medieval world.