How do photons get into the eyes?

Yes - we are surrounded by a "sea of photons".

An individual object that reflects light (let's assume a Lambertian reflector - something that reflects incident photons in all directions) sends some fraction of the incident photons in all directions. "Some fraction" because the surface will absorb some light (there is no such thing as 100% white).

The propagation of photons follows linear laws (at normal light intensities) so that two photons, like waves, can travel on intersecting paths and continue along their way without disturbing each other.

Finally it is worth calculating how many photons hit a unit area per unit time. If we assume sunlight, we know that the intensity of the light is about 1 kW / m$^2$. For the purpose of approximation, if we assume every photon had a wavelength of 500 nm, it would have an energy of $E = \frac{h}{\lambda} = 3.97 \cdot 10^{-19}\ J$. So one square meter is hit with approximately $2.5\cdot 10^{21}$ photons. Let's assume your grey column reflects just 20% of these and that the visible component of light is about 1/10th of the total light (for the sake of this argument I can be off by an order of magnitude... this is for illustration only).

At a distance of 200 m, these photons would have spread over a sphere with a surface of $4\pi R^2 \approx 500,000\ m^2$, or $10^{14}$ photons per square meter per second.

If your pupil has a diameter of 4 mm, an area of $12\ mm^2$, it will be hit by about $12\cdot 10^8$ photons per second from one square meter of grey surface illuminated by the sun from 200 m away.

At that distance, the angular size of that object is about 1/200 th of a radian. "Normal" vision is defined as the ability to resolve objects that are about 5 minutes of arc (there are 60 minutes to a degree and about 57 degrees to a radian). in other words, you should be able to resolve 1/(57*(60/5)) or about 1/600 of a radian. That's still lots of photons...

Finally you ask "how do we distinguish what photons are reflected from what"? For this we have to thank the lens in our eye. A photon has a particular direction, and thanks to the lens its energy ends up on a particular part of the retina (this is what we call "focusing"). Photons from different directions end up in a different place. Nerves on the back of the retina tell us where the photons landed - and even what color they were. The visual cortex (part of the brain) uses that information to make a picture of the surrounding world in our mind.

It's nothing short of miraculous.

Feynman has a fascinating talk about light:

If I’m sitting next to a swimming pool, and somebody dives in, I think of the waves: these things that have formed in the water. When lots of people have dived into the pool there’s a great choppiness of all these waves all over the water.

To think that it’s possible, maybe, that in those waves there’s a clue as to what’s happening in the pool. That some sort of insect or something with sufficient cleverness could sit in the corner of the pool and just be disturbed by the waves, and by the nature of the irregularities and bumping of the waves have figured out who jumped in, where, and when.

And that’s what we’re doing when we’re looking at something. The light that comes out is waves, just like in the swimming pool except in three dimensions instead of the two dimensions of the pool. It’s going in all directions. And we have a 3mm black hole into which these things go, which is particularly sensitive to the parts of the waves that are coming in a particular direction. It’s not particularly sensitive when they’re coming in at the wrong angle, which we say is from the corner of our eye. And if we want to get more information from the corner of our eye we swivel this ball about so that the hole moves from place to place.

Then, it’s quite wonderful that we see. That’s because the light waves are easier than the waves in the water, which are a little bit more complicated. It would have been harder for the bug than for us, but it’s the same idea, to figure out what the thing is that we’re looking at at a distance.

And it is kind of incredible, because when I am looking at you, someone standing to my left could see somebody who is standing on my right, and that the light can go right across these waves, the waves that are going this way and that. It is just a complete network.

Now it’s easy to think of them as arrows passing each other, but that’s not the way it is, because all of this is something shaking (it is called the electric field), but we don’t have to bother with what it is. It is just like the water height that is going up and down. So some quantities are shaking about here, and the combination of the motion that is so elaborate and complicated then that results in what make me see you. And at the same time, completely undisturbed by the fact that there influences represent the other guy seeing the other on this side.

So that this is a tremendous mess of waves, all over in space, which is the the light bouncing around the room, and going from one thing to the other, because of course most of the room doesn’t have 3mm black holes: it is not interested in that light, but the light is there anyway: it bounces off it, it bounces off that, and all of this is going on, and yet we can sort it out with this instrument called an eye.

But besides all that, these little waves I was talking about in the water, maybe they are so big some of them and then you can have slower swashes which are longer and shorter. Perhaps our animal who's making this study only uses waves between this length and that length. So it turns out that the eye is only using waves between this length and that length, except that those two lengths are hundreds of nanometers.

And what about the slowest swashes, the waves that go more slowly that happen to have the longer distance between crest to trough? Those represent heat. We feel those, but our eyes don’t see them focused very well; we don’t see them at all. The shorter wave is blue, the longer wave (as you know) is red, but when it gets longer that that—we call it infrared. All of these is in there at the same time; that’s the heat. Pit viper that get down here in the desert, they have a very little hole so that they can see longer waves, and pick up mice, which are radiating their heat in the longer waves (but their body heat) by looking at them with this eye, which is the pit of the pit viper.

But we can’t, we are not able to do that. And the these waves get longer and longer, and (all through the same space, all of this things are going on at the same time), so that in this space there is not only my vision of you, but also information from from Moscow Radio that’s being broadcasted at present moment, and the seeing of somebody from Peru!

All the radio waves are just the same kind of waves, only they are longer waves. And there’s the radar, from the airplane which is looking at the ground to figure out where it is, which is coming through this room at the same time.

Plus the X-rays, and cosmic rays, and all these other things, which are the same kind of waves—exactly the same waves—but shorter/faster, or longer/slower.

It’s exactly the same thing, so this big field, this—this area of irregular motions of this electric field, this vibration, contains this tremendous information, and it’s all really there: that’s what gets you.

If you don’t believe it, then you pick a piece of wire and connect it to a box and in the wire the electrons would be pushed back and forth by this electric field, swashing just at the right speed for the certain kind of long waves, and you turn some knobs on the box to get the swashing just right, and you hear Radio Moscow! Then you know that it was there. How else did it get there? It was there all the time. It is only when you turn on the radio that you notice it.

But that all these things are going through the room at the same time which everybody knows, but you gotta stop and think about it to really get the pleasure about the complexity—the inconceivable nature of nature.