In our galaxy alone (The Milky Way), there are estimated to be at least 100 billion stars.
But our galaxy certainly isn't the only one, and coming in at over 120,000 light years in diameter, is considered to be around average in terms of sheer size by the standards of the universe.
The next closest galaxy, Andromeda (or M31 as it's otherwise known), is over 50,000 light years more in diameter, and is estimated to contain a total of 1 trillion stars - that's 1,000,000,000,000!
This is the famous "Hubble deep field image" that illustrates the vastness of space... Those lights aren't individual stars, rather entire galaxies.....

So in order to answer the question of how many stars there are in the universe, it's important to consider how many galaxies there are.
I must admit, this question is an impossible one, as we have absolutely no idea how big the entire universe is.
We can only make estimates based on interpreting what we can see, and the truth is that most of the universe is completely out of our reach (for the time being at least.)
But why?
The limitations of light
Light travels incredibly fast - 300 million meters every second through an empty vacuum such as space.
However, even light travelling at that speed from what could be a massive proportion of the universe simply hasn't had enough time to reach us yet.
The universe is supposedly around 14 billion years old and using the most accepted model of how the universe began (at the time of writing this), the Big Bang Theory, it's suggested that everything in the universe, including space-time itself, expanded outwards from a single "point" (although in the absence of space itself, you can see how it would be difficult to define where this would've happened) uniformly in all directions.
With energy-matter being accelerated in all directions, from a single reference point such as our own galaxy, the light coming from some of that matter simply hasn't had enough time to reach us yet.
Therefore, we can imagine an invisible sphere that extends outward from the observer (in this case us) all the way to the distance at which light has had enough time to reach our eyes.
What we end up with is the "observable universe".
Every point in space has its own observable universe, and what lies beyond it, well nobody knows...
So we can have as many estimates as we like at how many stars there are in the observable universe, but the entire universe?
That would no longer be estimating, rather completely guessing.
The latest estimate as of 19/03/2023 for the total number of galaxies in our observable universe is a range of 100-200 billion galaxies.
So how many stars is that?
Well, if we take the Milky Way as an average sized galaxy, and multiply its number of stars by the number of galaxies, then we end up with a range of 10,000,000,000,000,000,000,000 - 1,000,000,000,000,000,000,000,000
That's 10 thousand billion billion - 1 trillion trillion stars in the observable universe.
Naturally, you might be asking yourselves how astronomers even come come up with the number of stars in our galaxy, and galaxies in the observable universe, so let's take a look at those two methods now.
The method
They send huge telescopes like the Hubble, or the more recent JWST (James Webb Space Telescope) into space and use their optics to collect as much light as possible in all directions.
By the way, if you're familiar with terms like aperture and focal length, then you might be interested to know that the JWST has an aperture of 6 meters (aperture means the diameter of the mirror that collects light), and a focal length of 131 meters, giving it an f/ratio of 20.2!
Needless to say that's A LOT of power in terms of its ability to collect and magnify the light coming from distant galaxies.
Now consider the following thought experiment....
In an alternate universe, I hand you a huge bucket full of ping pong balls and offer you a million dollars to accurately count how many ping-pong balls there are in that bucket...
Well...to be honest, for a million dollars you'd probably sit there all day and count them individually to be certain, but let's say there's some time limit to prevent that, then you'd probably end up doing something like this.
I've not given you any measuring instruments...
You would scoop as many balls as possible with your hands and arms, count them individually and try to estimate how many "scoops" you could get out of the whole bucket.
Then multiplying the two numbers together would give you an estimate for the total number of ping pong balls in the bucket.
Well, a similar kind of process happens when astronomers attempt to get an estimate for the total number of galaxies in our universe:
They take long-exposure pictures with huge telescopes such as the ones mentioned above, count how many galaxies can be seen in that individual picture, then work out how many pictures could taken with none overlapping each other in the 360 degrees that we have access to.
Just like with the bucket example, they then multiply the two together and voila...
This method relies on making a certain assumption about the universe - that it's homogenous.
While perhaps sounding a bit complicated at first, it's really not, and simply says that the universe appears roughly the same from any position on a large enough scale.
In other words, there are no specific areas of space where the number of galaxies is extraordinarily high or low.
And how about counting stars?
That's a bit more complicated, as stars aren't evenly distributed through the universe like galaxies are (galaxies aren't distributed everywhere per say, as they often come together to form massive groups), but rather collected in dense packets called galaxies, ranging in size and shape.
So we can't simply take pictures of galaxies and count how many stars there are in them - there's simply way too many stars.
What we can do, however, is analyse the luminosity of galaxies (how bright they are) to determine how many stars would roughly have to be present to create that level of brightness.
Astronomers take a picture of the universe at a certain angle as described above, count how many galaxies are present in that 1 photo and then calculate how many stars there are via the luminosity method.
Then we can multiply that number by the number photos that we could take in all directions (360 degrees), ending us up with the total number of stars in the observable universe.
In the case of assuming that the Milky Way is of average size and hence contains an average amount of stars, as I did earlier, then that's a whole lot simpler, as we can estimate the total number of stars in our galaxy by analysing the rotation of the night sky (in a very dark location) and calculating the luminosity of the light that we see.
Thanks for reading!