Assume we know theism is true. Can we theists ever tell that our prayers have been answered? I pray for E and E occurs. Can I ever know that God acted on my prayer rather than E occurring completely independently of my prayer? It turns out that the answer is simpler than one might think, and that we can know this much more often than one might think.
Consider the property of Reasons Maximalism (RM) that an agent might have. An agent has RM if and only if whenever she chooses an action A, she chooses it on account of all the unexcluded reasons she is aware of in favor of A. Suppose, for instance, that I have a duty to visit a sick friend and I enjoy her company even when she is sick, but, on the other hand, it's a long drive and the hospital is depressing. Nonetheless, I do visit her. If I don't have RM, I might be visiting her only out of duty or only for pleasant companionship. But if I have RM, I am visiting her because of both duty and pleasant companionship. And if I have RM and decide not to visit her, then I will decide to do that because of both the long drive and the depressingness of the hospital.
I submit that God has RM. Being perfectly morally good and perfectly rational, in every decision God takes into consideration all the unexcluded reasons he has. Of course, in the end, it may not be possible for him to act on all the reasons, because some of the reasons will pull in different ways. But his choice will have been made on the basis of all the reasons he is aware of in favor of it. Moreover, in the case of an omniscient being, the reasons she is aware of in favor of A is the same as the reasons she has in favor of A. Thus, God chooses A on the basis of all the unexcluded reasons he has that favor A.
Now, that I've requested something good and grantable is always a reason to grant the request. In rare cases, it will be an excluded reason--perhaps I earlier authoritatively commanded the person to stop granting my requests for a day. But I cannot think of an exclusionary reason God might have against considering our requests for good things. (If God promised not to hear our requests, that would be an exclusionary reason, but he made no such promise.)
I don't know exactly how to analyze "grantable". One class of non-grantables are states of affairs ruled out by divine promises. Another class of non-grantables are states of affairs that cannot be brought about, whether because they are metaphysically impossible or because they are metaphysically necessary. It may also be that people's free choices are non-grantables. However, perhaps when we pray that x (where x is not God) might freely do A, God reinterprets our prayer charitably as a prayer that x be given lots of reason to do A, and that is a grantable. I do not know whether things that God has already promised are grantables, but I am inclined to think they are (cf. the sick friend visit case).
So, our requests for grantable good things are always an unexcluded reason for God to grant the request, and God being omniscient is aware of this. Moreover, God is a concurrent cause in all good events (in fact, in all events, because evil is a mere privation, but nevermind that), so that all good events count as caused by God. Therefore, by RM, if I pray for grantable good, and God brings about the request, then God produces the good in part because of the request. So, a sufficient condition for my knowing that an event has happened as a result of my request is that (a) I prayed for it, (b) it was good, (c) it was grantable and (d) it occurred.
In particular cases, these conditions are very commonly satisfied. If you pray for someone's safety during a trip, and she returns safely, she does so in part because of your prayers. If you pray that you find a lost object, and you do find it, you find it in part because of your prayers. If you pray that a friend might recover from an illness, and she recovers, she recovers in part because of your prayers.
