You can definitely make this look more natural, but it will take some work!
Obviously, that wood fencing around the pond will have to go. I'm guessing it's there to prevent rocks from falling into the pond, but we can find a better solution than that.
To truly naturalize the edges, you'll want to have a couple large boulders, a lot of medium-sized rocks, and small rocks. Most guides I read suggested using stone of the same type, but at least here in the mountains where I live, I often see sandstone of varying shades, slate, granite looking rock, all in one pile.
Most natural ponds will have rounded stones due to weathering. This is also a rule I ignored with my pond, because I'm cheap and I got my rocks for free from a friend, so I wasn't about to be choosy!
The key is that you don't lay down the stones in any repeating pattern, and you make sure you juxtapose rocks of various sizes right next to each other. You want to really show off the size difference. Often people will choose stones of all the same size and create a ring around the pond. It's called a "pearl necklace" in the industry, because it looks like a pretty row of pearls (though it can also be done with flat, stepping stone type rocks, not just round ones.
You can use waterfall foam to stick rocks of varying sizes together and prevent the little ones from falling into the pond. This will also help prevent runoff from the yard from leaking into the pond. REGULAR YARD FERTILIZER AND PRODUCTS CAN BE DEADLY TO FISH. Keep in mind that whatever you choose to grow plant-wise near the pond, you must be extremely careful with what you use to feed it.
Another tip for creating a natural look is to use dirt and plants around the border, not just rocks. Apparently the average shoreline is only 40% rocks or something like that. In an artificial pond, we can get away with using about 60% before it looks artificial (according to some video I watched on Youtube, anyway). This is something that I had a lot of trouble with and ultimately decided to keep a ring of rocks around the pond, but to have dirt come right up against the rocks, and then to grow plants in the dirt. My hope is that over time the plants will encroach closer and closer to the pond liner, obscuring the rocks somewhat and creating a more natural look over time.
The waterfall you've got there could use some work if you want it to look more natural. It, too, needs rocks of varying sizes. Typically waterfall construction is done by laying down a flat stone, which will create a ledge, and having two taller, rounded stones on either side of it to pinch and direct the water flow. This is repeated, and pockets of gravel, little pools, or divisions in the water can be added as desired to lengthen out the waterfall stream (good for sound quality and aerating the water!), create a place where small bog plants can be grown (like creeping jenny, parrots feather, etc.), and overall create a more visually appealing, natural look. The key with waterfall construction is to avoid going too high. Allow the hill the waterfall comes from to slope very slowly, over a huge surface area of the yard. this will create the appearance of a natural spring emerging from the depths of the earth, rather than an odd volcano looking mound spewing out water from nowhere.
All of the changes above I've mentioned will require a lot of effort, and could potentially be expensive (landscaping rocks cost so much!). But even removing all that excess slate, the mini wood fencing, and adding some pond plants of varying styles (grass/reed-like, for example) around the edges would make a huge difference to the overall appeal of that pond.
As others have already said, the important thing is to really look it over, be patient, and figure out what you want. In the end, I opted to not go for an entirely natural look. As I said, I still have a ring of rocks around my pond. I still have some liner showing underneath those rocks along the inside of the pond before reaching the water level because the edges are sheer. You can see planters inside my pond, none of which look very natural. But I did want my waterfall to look and sound as natural as I could make it. It is kind of the artistic centerpiece the pond, so to speak. And it was very important to me to have places where I could sit up and close to the pond. I have two jumbo boulders and a wooden "dock/deck" for that reason. And it was important for me to have the chance to grow plants all around the pond in hopes of naturalizing it somewhat, so I made sure my garden dirt comes as close up to the pond as it can (without too much of it falling in because that makes the water murky). Think over what your priorities are when it comes to how you want to interact with the pond. The person who made that pond before you obviously did't intend to soak their feet in the water, for example. There's really nowhere to sit comfortably up close and personal with that pond.
