Many theists believe in miracles.
It's not always easy to define 'miracles.' One of the most common ways is this:
A miracle occurs when a deity intentionally violates a law of nature.
This is a pretty good definition, although there's room for quibbles, as usual. If it was really a "law" of nature, how could it be violated? Can there even be laws of nature in a world that is controlled by a deity? We'll set those worries aside for now.
Here's an alternative definition:
A miracle occurs when a deity causes something that would otherwise be extremely improbable to happen.
One might simply define a miracle as a deity's intentionally acting in the world. That could be a good definition, but if we're just talking about a mundane occurrence, it won't be much help to theists, since it'll be obvious that there's no need to say a deity explains the event. So we'll be okay by focusing just on the miracles that seem to be violations of the laws of nature, or otherwise improbable events.
Some theists think we are justified in believing in miracles. By the above definition, if miracles exist, then a deity exists. So the theist's job would be to prove that we are justified in believing in miracles.
Why believe in miracles?
It's easy to find a host of examples from history of potential miracles, even when we confine our focus just to Christianity. Many people report miraculous occurrences. One major source of such accounts, of course, is the Bible. Jesus is alleged to have performed miracles. In addition, the Roman Catholic church holds that one of the ways of recognizing a saint is if God performs a miracle in response to a prayer to a deceased person.
It doesn't seem possible to verify with certainty that some event was a miracle. Therefore, it's unlikely that there's a deductive argument for theism here. If it is possible to argue for theism from the existence of miracles, it's probably by an abductive argument, an argument to the best explanation. The argument might look like this:
(1) There is a set M of miraculous events.
(2) The best explanation for M is that a deity intentionally brought it about that M occur.
(3) Therefore, probably, a deity exists.
I think there's room to question both of the argument's premises.
One thing we notice fairly soon about miracles is that most of them don't clearly seem to be violations of laws of nature. Often, for example, people think that being cured of a deadly disease, or saved from a dangerous natural disaster or accident, is likely to be a miracle. Now, certainly the Bible seems to contain reports of lots of actually miraculous events, such as turning water into wine. But of course lots of stories from that time (and from many centuries after) contain reports of miraculous or magical events. Perhaps it was just a miraculous sort of time. But since we generally discount stories about magic, we should generally discount Biblical stories of miraculous events. That doesn't mean we should be sure that they're false. But it does mean that we should consider them to be evidentially at an initial disadvantage. We would be at least prima facie justified in believing that at least some of the stories are as likely to be true as other old stories about magic.
What about highly improbable events? Well, humans are notoriously bad at estimating probabilities. We suffer from all sorts of selection effects, priming effects, and the like. For example, people will commonly think that the set of five playing cards (e.g.) 3D, AC, 10H, 9D, 6S is more likely to occur in a random drawing than the set AD, KD, QD, JD, 10D. But they're both equally likely. People often don't fully realize that in a big enough world, unlikely things will happen to some people sometimes.
Therefore, I don't think there have been nearly as many miraculous events as some people think there have been. It's difficult to see such reports as anything more than the other myths, fairy tales, and legends that have been passed down to us in the last millennia.
The Humean Anti-Miracles Argument
There is general problem with any appeal to miracles, one discovered at least as early as David Hume. To begin with, it's reasonable, in general, when you encounter a mysterious event, to try to explain that event with information you already have. For example, if you already know that such events are commonly caused by some cause C, perhaps C is a good explanation for the event you're currently thinking about.
We can imagine a world in which there were verified miracles. In this world, perhaps, a deity was closely involved with the day-to-day lives of the humans in the world, and could prove to them that it was responsible for various events. Perhaps we can sort of imagine a world, even, in which there was some knock-down argument that some event was a miracle, even if no deity testified to us that it was.
We can also imagine a world in which no one ever told tall tales, recorded legends, created hoaxes, or made mistakes. There could be a population of much less credulous humans who had much more accurate ways of forming beliefs.
Of course, neither of those is the case in the actual world. We don't have any verified miracles. What we do have, unfortunately, is a lot of verified non-miracles that might appear miraculous. For example:
Mistaken perceptions; mistaken memories; hallucinations; hoaxes; mistaken textual recordings; mistaken translations; myths; legends; lies; events that seemed miraculous but later turned out to have scientific explanations.
We know of a great many examples of those. And some of those could easily appear miraculous. Therefore, if we have no verified miracles, and tons of verified non-miracles that seemed miraculous, then for any alleged miracle, it's more reasonable to believe that it wasn't an actual miracle.
One way someone might respond to this argument would be to say that all it shows is that probably, not all alleged miracles are real miracles. But isn't it still fairly likely that at fewest one of them was an actual miracle? I don't think so. We just have no way to estimate the probability that something is a miracle without having at fewest some verified miracles. As an analogy, consider the hypothesis that some of the apparent humans walking the earth are actually aliens in disguise. Yes, that seems unlikely, but surely within seven billion humans, it's likely that one is an alien in disguise, right? No--at least, not until we know how common disguised aliens are.
This objection seems to challenge both premises, since some of the alternative explanations are that the event wasn't really miraculous at all, and others are that it was, but it had an obscure scientific explanation.
Explaining these events
Even if we were to think that some genuinely miraculous events have occurred, and they weren't just misrememberings or misrecordings, how likely should we say it is that some deity caused the event to occur?
Well, the explanation that it was a deity suffers from several well-known problems with that explanation in general. For one thing, it doesn't seem to help us make the world a simpler, more explainable place in general, since now we have to explain the existence of that deity.
Worse, though, we run up against the problem of the a priori and empirical improbability of a deity, especially of one of the classic monotheistic deities. Such a being would have many very rare or unique attributes. However, we've already noted that many obscure but scientific explanations can explain otherwise miraculous-seeming events, and those explanations tend to have much higher probabilities; they tend to be overall propositionally simpler, and we tend to have experience of observing those explanations in the past, or at least discovering the particles and fields that would be required to make those explanations work.
These objections do not prove that no miracles have ever occurred, but they seem to show that we should always think it's more likely that some alleged miraculous event was not a miracle after all.