Here's how to safely take easy pictures of the Moon and the Sun; it's how most of us get started in Astrophotography!
Lunar and Solar
Most of us have taken a picture of the Moon with whatever camera was lying around at the time. For many of us, it was with our smartphone. The Sun is different. Aiming your smartphone (or any other camera) at the Sun without proper protection is a recipe for damaging not just your camera but your eyes as well - permanently! So always take proper precautions when taking pictures of the Sun, and make sure you check your filters for any damage before using them.
Lunar
In theory, the moon should be able to be seen every day from the Earth. Sometimes when it's night, and sometimes in the day. But when the Moon is new, meaning, when it's between the Sun and the Earth, it can be hard to see. So a good rule of thumb is that you should be able to see the Moon about 75% of the time, depending on your local weather. This makes the Moon an easy target to image, because it's always there. It's also really bright and really big, which makes it easy to find and relatively easy to photograph. But its size is deceptive. If you have a good camera on your smartphone, the picture of the Moon you took might come out okay, it was probably not what you hoped it would be. To really take pictures of the Moon well, you need to up your game a bit.
When we look at the Moon with our eyes, we sometimes see foreground objects between us and the Moon. Our brain fools us into thinking the Moon is bigger when it's near the horizon, behind these objects. Even when it's straight overhead, we think the Moon is pretty big. And it is, compared to stars and planets! But it still occupies just a tiny bit of your camera sensor. On a DSLR or Mirrorless camera with a 100mm lens, you can expect it to look like this. All things considered, that's not very big. Even a 400mm lens would only make it look twice as wide/tall. With modern cameras like a Canon T7 or similar, however, we have a lot of pixels to work with and can zoom that 24MP image (which starts out as 6000x4000 pixels) into something like 1500x1000, which is an 8x zoom. The Moon will look something like this second image (this is artificially created, not a real photograph). As you can see - it's starting to look pretty good. 
Improving your Lunar Astrophotography
To do lunar astrophotography well, you really need a tripod. If you haven't already read the Essential Gear and Setup article, check that out. It has some basic options that will work well for lunar, solar, and wide-field astrophotography. Using a tripod will help you keep steady when you take the shot. This lets you take a longer shot at lower ISO settings to get less noise in your final image and more signal. The signal-to-noise ratio represent how much of a good thing (the signal) there is compared to how much of a bad thing (the noise) there is. You want this number as high as possible, so having a tripod and using a shutter release (or a self-timer mode if your camera has it) will let you take better pictures by keeping steady, using lower ISO settings, and more accurate exposures. See the Camera Settings for Astrophotography article for more information on what would make some good settings for general Lunar astrophotography.
Lunar Eclipses
Unlike a Solar Eclipse, you don't need any special filters to take pictures of the Moon when the Earth passes in front of it. Also, lunar eclipses happen much more frequently than solar eclipses, and you don't have to be in a very specific spot on Earth to see them - just "on the dark side of the planet." Taking lunar eclipse pictures is just like taking normal lunar pictures except you'll want to maintain proper exposure settings to make sure your camera doesn't try to adjust the brightness as the Moon darkens. Since it takes hours (as opposed to minutes for a solar eclipse) you have time to play with the settings during the eclipse. So keep an eye on web pages like timeanddate.com for when you'll be able to see one, and get your gear set up! You can practice in the nights before to make sure you have your overall exposure dialed in, so you don't have to fiddle as much on the eclipse night. If your camera has an intervalometer setting, where it automatically takes pictures every few minutes, set it to 5 or 10 minutes and sit back and enjoy while your camera captures the event!
Solar
Remember - taking pictures of the Sun is dangerous! Always use proper filters, equipment, and protection!
NEVER look at the Sun without proper filters, equipment, and protection!
Taking pictures of the Sun sounds simple - point your camera at the big bright thing in the sky and take a picture. But it's not. The Sun produces a lot of energy. We see that energy as light, and we feel it as heat. There's also energy we can't see or feel directly. Some of it is in the form of ultraviolet (or "UV") radiation, the same stuff that burns your skin when you spend the day outside without sunscreen. If you aim your camera at the Sun, the lenses on your camera focus the Sun's energy - UV, light, heat, and everything else - onto a small area - your camera sensor or your eye. That UV radiation is the main problem, since focusing it on a small area can cause sensor damage. If the sensor is your camera, you'll likely have a burn-in spot that never goes away and always leaves a dot or circle on future images. In the worst cases, you can literally melt parts of your lens, camera, or sensor and destroy it. If the camera is your eye, you can end up with many symptoms, including permanent blindness. For more information, see this article about Solar Retinopathy from the Cleveland Clinic.
Proper Filters, Equipment, and Protection
Thankfully, scientists and engineers have figure out what the proper filters, equipment, and protection is. And they're relatively cheap. Here's a quick look at what it all means.
Filters
Remember those eclipse glasses you got in 2017 and 2024? If they were properly made, those are considered "solar safe" filters. These tend to leave the Sun looking orange due to what bands of light they filter out. If you don't like that look, there are also "white light" solar filters that show the Sun as a white disk. You can buy solar safe filters for your camera or make your own. I recommend purchasing them so you know they're safe, but I've made many solar filters through the years once I knew the proper technique and purchase the proper supplies. A good source of these solar filters is High Point Scientific. I will earn a small referral fee for anything you purchase from them (see my Support page for more info). You'll want to find your telescope or the outer diameter of your camera lens in millimeters. It will give you some suggestions on a good solar filter. Remember that "OD" means "Outside Diameter" and can be easily measured by putting your lens down face-first onto a piece of paper and tracing a circle around it. Measure the diameter of that circle in mm and go find your filter!
Equipment
This refers to a "next stage" of solar photography advancement beyond filters that you stick on the front of your lens. And while it makes for more exciting photographs, it also puts more of a dent in your wallet. There are actual telescopes with filters built-in that are designed to look at (and take pictures) of the Sun. I have one, a Coronado SolarMax II 60 that is designed for viewing the Sun in a very specific wavelength of light called Hydrogen-alpha, or Ha. This isn't a cheap option, but if you want to see images like this one then that's what you'll need to get. Plus a solar camera and probably a tracker and... well, as I said, this is a more expensive option. All in, I think I have about $3000 spent on scope, camera, tripod, tracker, and auto-focus unit, not to mention a laptop or dedicated astro PC to control it all. So this is definitely not for most beginners. But it's something you can aspire to if Solar astrophotography excited you!
Protection
The number one thing you need is proper filters. Make sure you have them, properly connect them to your telescope or camera, and you are good to go. But you also need to protect yourself. Remember, you're taking pictures of the Sun, so you're doing it while the Sun is shining in (hopefully) bright daylight. So get some sunscreen, sunglasses, maybe a nice sunbrella, and make sure to stay hydrated. It can be both sunny and cold, so wear appropriate clothing. If you're hiking somewhere to get a good view of the Sun outside of a smoggy city, bring snacks, prepare for the wilderness, and make sure someone know where you are and when you expect to be back. This stuff should all be obvious and most of us can simply put the scope on the picnic table in the backyard and start imaging, but you need to do what is right for you - not what's right for someone else when it comes to taking care of yourself when you're doing astrophotography. Luckily, it's daylight so you don't have to worry about doing all of that in the dark like a normal Astropotamus does when taking nighttime images!
Solar Eclipses
Solar Eclipses are a completely different topic that we'll discuss elsewhere.
Conclusion
Taking pictures of the Moon and the Sun is not only rewarding, it can be simple and straightforward. I won't go so far as to say "easy" because, year after I started on this journey, I'm still learning how to do both well. But it is "easy enough" to get started, and other than a solar filter, you probably already have all the gear you need to get started. Moon pictures are always favorites because everyone knows what it looks like so they always love seeing it through someone else's camera lens. Solar images can be awe-inspiring as well, especially if you bite the bullet and go for a dedicated solar setup. Most of us Astropotamuses take pictures at night. Which is fine. There's a lot to see there. But opening up the day to both solar and lunar imaging (remember - you can see the Moon in daylight!) provides almost 100% more time for taking astrophotography pictures!
Until next time, clear skies, and I'll see you in the dark (or light)!