When Buddhists pray, who do they pray to?

[Been There]

They pray to no one.
The "prayers" are actually imprints they are setting into their brains .. thoughts, ideals, concepts, visualizations of qualities-of-being (such as visualizing compassion or wisdom, or dedication to the practices ... etc).

In Tibetan Buddhism these qualities are personified as the "deities" .. Manjushri, Chenrezig, etc. Note that some Buddhist practitioners LIKE the idea of higher powers .. well, to each their own. If they want to, they can pray TO some entity.
You get mixed messages from the teachers ... for instance, one lama was dying of cancer and taught right up to less than a week before his death. You couldn't tell he was sick, but once or twice during a 2-hour class, he would briefly close his eyes and sit still for a minute. Then he would open his eyes and apologize, saying he'd been talking to his teachers. Now, did he mean that literally? Or figuratively? In Buddhism ANY person OR situation that is difficult is called our "kind teacher" because it gives us the opportunity to do our practice. The lama never defined what he was referring to.
Same thing with the deities ... one can see them as entities, one can see them as metaphors. They are taught in such a way that you can take it either way.

But make no mistake .. the teachers/lamas/geshes/bikkhus I have heard teach .. they ALL say that ONLY you can reach enlightenment, that NO higher power can do it for you. By extrapolation, what use would it be to pray to any deity or to Buddha, if they cannot help us?
And I asked my own lama if saying the "Medicine Buddha" puja (ritual) would help someone I knew who was sick .. he shook his head and told me that it only helped me, by increasing my compassion for others. So in Buddhism prayer has no metaphysical power.

This is probably not as clear-cut an answer as you would like .. but the eastern monks seem to think it is rude to correct or contradict people. When someone in the class stands up and angrily says that what the teacher is saying is wrong, the teacher sits there and gently looks at them with great love and says, "You may be right", or "I'll have to think about that".

You see, Buddhism is an inner journey. The teachers are our guides, but they don't tell us what to think or how to feel. They give us the teachings, but don't insist we "believe" them or even follow them. They give us the meditations, the pujas, the various practices, and tell us to go do them and see for ourselves what happens.