It is a myth, and false gossip really, that the Reformed faith turns a cold eye toward prayer. “Calvinism cannot account for the Bible’s portrayal of prayer as a cause of God’s answers to prayer,” says this group. They even supply a meme! (I have been Reformed for decades and do not recognize this parody of my prayer life!)

Nor am I happy with non-Calvinists who tell me that my life of prayer is incoherent and inconsistent with my theology. In fact, I insist that people of any group, beginning with my own, should assume at the outset that we might not understand what people of other groups believe. (For my part, I would affirm that Arminians too believe in God’s sovereignty, and his foreknowledge of all events; thus I cannot see how their viewpoint makes prayer any easier or more logical than my own; but perhaps I am mistaken!)
But, in fact, even John Calvin denounced this false image. In his commentary on James 5, that the prayers of a righteous man “availeth”, he says “In case anyone should think that there is no benefit gained by others praying for us” and then shows how prayer is effective. And included in his Institutes a whole section on the topic. Rather, our dependence on our Sovereign Father makes us even more likely to run to him in prayer.
Let’s listen to Calvin himself, with some updated language on my part. He abhors the idea that Fate has determined all things, calling it pagan. Rather, God is sovereign; he is not bound by Fate, nor does his decree tie his hands, so that he cannot answer our prayers.
Those who want to discredit this doctrine [of the divine decree] disparage it by comparing it with the Stoic dogma of Fate. The same charge was brought against Augustine. We don’t want to argue about words, but we do not allow the term ‘Fate’, both because it is among those that Paul teaches us to avoid as heathen innovations and also because the obnoxious terms in an attempt to attach stigma to God’s truth. From Calvin’s Institutes I, xvi, 8
That means that God is the Most Free one, who can answer our prayers as he wishes. To imagine that God is straitjacketed by Fate or even his own decree is to commit the most egregious error about who he is. If we cannot figure out how to reconcile this with the divine decree, that is because of our own limitations; it does not invalidate the need for prayer.
But, someone will say, does God not know, even without being reminded, both the troubles we have and what is best for us, so that it might seem superfluous that he should be stirred up by our prayers – as if he were drowsily blinking or even sleeping until he is aroused by our voice?
But they who reason in that way do not understand why the Lord instructed his people to pray, for he ordained it not so much for his own sake as for ours.
Now God desires – as is right – that we render due honor to him, as we recognize that everything we desire and think is best for us comes from God, and so we confirm this by praying. So when we offer the sacrifice of prayer, we not only worship him, but the benefit returns to us.
Accordingly, the holy fathers, the more confidently they extolled God’s benefits among themselves and others, were the more keenly aroused to pray. It will be enough for us to note the single example of Elijah, who, sure of God’s purpose, after he has deliberately promised rain to King Ahab, still anxiously prays with his head between his knees, and sends his servant seven times to look [1 Kings 18:42]. He prayed this way, not because he thought his prophecy was not going to come about, but because he knew it was his duty, lest his faith be sleepy or sluggish, to lay his desires before God. So, we grow dull and stupid about our own miseries, but still he watches and keeps guard on our behalf. And sometimes even helps us without our even asking, but still it is very important for us to call upon him: First, that our hearts may be fired up with a zealous and burning desire to always seek, love, and serve him, while we become accustomed in every need to flee to him as to a sacred anchor. Secondly, that there may enter our hearts no desire and no wish at all of which we should be ashamed for him to see, while we learn to set all our wishes before his eyes and even to pour out our whole hearts.” From Calvin’s Institutes III, xx, 3. For the whole section, go here.
“John Calvin and Prayer,” by Gary S. Shogren, Professor of New Testament, Seminario ESEPA, San José, Costa Rica