Tonight I decided to take a couple of shots with my Nikon D3200 on a tripod for the first time. When I was looking at them on my computer, I noticed these dots. Are these stars or just noise? I highly doubt they're stars because I live in quite a light polluted area in Miami, but it doesn't hurt to ask and learn if it even is noise or something else. I should probably mention I've been more heavily involved with all things photography and cameras for about a year now and I'm just in the beginning stages of photography, so obviously the picture you see in this post isn't magnificent in any way.
You can filter out faint stars from the noise by using the fact that stars will be slightly blurred. You can see this clearly if you look at Mars in your picture which as pointed out in szulat's answer, is to the left of the Moon in your picture. Due to the rotation of the Earth during the exposure all the stars will appear as trails if you zoom in. Also, the focus will not have been perfect, so the trail will have a thickness of a few pixels. These trails will be very small circle segments that will have the Pole star as the center. Noise will appear as small dots that are just one or a few pixels wide (due to the way raw files are processed, a large fluctuation in the gray value at one pixel can spill over to the neighboring pixels).
It is possible to take astrophotography shots without star trails. However, this shot does appear to contain mostly, if not all grain. I would recommend that next time you try shooting at night, you start by seeing if you can find a place with less light pollution. You can avoid noise with longer exposures (look into getting a shutter remote if you don't have one). That tactic will also gain you star trails. If you're looking to avoid the stair trails, you'll have to find a good balance of aperture and ISO to accommodate for the faster shutter speed. I have found this tutorial to be extremely helpful no matter which technique you'd like to use: https://expertphotography.com/the-ultimate-guide-to-landscape-photography-at-night/
Mostly just noise. There are some stars, but their signals are so weak they are barely higher than 1:1 SNR (due to both light pollution, as well as camera noise which comes from read noise and dark current). A lot of what might look like stars is also likely just hot pixels due to dark current, which can be ludicrously high on DSLRs (even these days, sadly, although it's getting better in general.)
When it comes to astrophotography, you are severely limited in terms of signal. To effectively image the night sky, especially in the city, you need to combine lots and lots of exposure (usually many individual sub exposures, aligned and stacked) to get anything usable. The dynamic range of objects in space tends to be massive. While you might have 9, 10, maybe even 11 stops of DR with a DSLR at higher ISO, you will often need 14, 16, or more stops of dynamic range to really bring out all the faint details (say the milky way).
Light pollution is obviously a problem. In your image, you also have the moon, which adds even more LP. It's best to image the night sky when it is as dark as possible. That means no moon, and later at night (when there are fewer cars on the road, fewer home and office lights on, etc.) The darker the skies, the easier it will be to get usable data in each exposure.
If you wish to image anything other than the moon, planets, or perhaps stars (such as the milky way or star clusters), then you will need to look into getting some kind of tracking mount. A basic tracker like the Star Adventurer, SkyTracker or Polari will usually do for basic DSLR+Lens imaging, and can allow you to get significantly more data without star trails or smudging from the motion of the stars across the sky.
The bigger the lens aperture the better as well (and I mean physical aperture here, entrance pupil, not relative aperture...which is such a horrible concept when it comes to astrophotography! ;P In this context, aperture refers to the literal, physical size of the opening in the lens...not F/#!! We always use f-ratio to refer to f/# in an astrophotography context.) So the fastest and best-corrected lens you can find will be best. In the case of ultra wides, wides, normals and moderate telephotos, the Samyang/Rokinon/Bower lenses actually tend to be the best performers (with a few rare exceptions). They are well corrected corner to corner, with minimal aberrations, and tend to be pretty fast with big apertures. A big aperture with a fast f-ratio will suck down more light in a given exposure time, which will help you reveal fainter details more quickly (it will give you a better SNR for any given exposure time.)
Once you are gathering enough light per exposure that some amount of the details you are after gets above the noise floor, you'll have an easier time creating interesting images of space, at whatever field of view. If you are in the city...and are most interested in ultra wide fields (i.e. milky way imaging)...get out of the city. Drive out about 30 minutes from the edge of town, and you'll be amazed at what even a basic camera and lens can get even on a fixed tripod. ;)