Even us cosmologists and computer scientists involved in the field don’t understand exactly how this process happens, but let me see if I can give you an answer from the viewpoint of this cosmologist.
First, you really need to understand how metals are produced, either from the Big Bang or cosmic rays to what is inside different types of stars, and how and how much or little is expelled when the star explodes. Even man-made metals/elements (Periodic Table below).
When a star explodes it scatters all its heavy metals, gold, silver, copper, iron, lead, tin, zinc, etc. in 360 degrees.
But not every star that explodes produces all the metals. Some stars produce only a few as this National Geographic article explains.
A version of the periodic table indicating the main origin of elements found on Earth. The main source of Earth elements above 103 (lawrencium) are manmade and are not included. (Credit: Cmglee - Licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.)
Now when a star starts to collapse on itself, this is when the heavy metals start forming from iron and the heavier metals stay closest to the star’s core, such as gold, which is why it is one of the rarest of metals. And a theory also states that since these materials are heavier, the are more likely bound by gravity which increases their escape velocity.
However, especially with gold and silver, physicists differ in how these metals are created, what type of star is needed to form them. Many do not give up any of the heaviest of metals.
For the longest time, a Supernova was required to produce gold, but a 2013 article in Smithonsian Magazine cites a study where astronomers now think that gold is produced when two neutron stars collide. These stars are the size of a small city but almost twice the density of our Sun.
Recently it was discovered that Earth was bombarded with radioactive Iron-60 from several close exploding stars as in this SpaceAnswers.com article. And even this article states that minuscule amounts were deposited on the Earth.
So the second thing that occurs when a star does explode, besides scattering its materials in all directions, it does not expel everything. The heavier the metal, the less of it the star will release. You’ll see why when you look at a cross-section of a star just as it is about to explode.
So in layman terms, you now know what is ejected from an exploding star, and in order of diminishing quantities. Another factor to consider is that heavier objects will tend to clump, or due to its mass, become gravity bound to each other. So gold will clump together with other gold elements, silver with silver, copper with copper, and so on.
As the accretion disk starts to form (it is now known that a supernova explosion does produce all the material to form new stars) this mixture of clumps of metals and dust (that eventually form rocks) will start attracting each other.
The problem is distribution out of the supernova. This is why in some areas on Earth you find tons and tons of gold in veins and large chunks, and other places not even a spec. It has to do with the early formation where the elements tend to stay together in clumps.
Copper, a more abundant mineral, is found almost all over the Earth, but it too will concentrate in certain areas for the same reason gold does. But because it is a lighter metal, more of it is expelled from the star, and it will concentrate in larger amounts in more places on Earth.
Now as the Earth is forming, is is molten. All the heaviest metals will sink deeper into the Earth than the lighter metals, which is why you can find copper very close to the surface, if not on the surface, and you need to dig 1/2 mile or more down to find gold and silver. Same with Iron. It also sinks deep into the center of the Earth.
Any planet that forms like Earth will have the same issues with metal distribution. It will not be uniform, as it did not come out of the star that way, and that makes the heaviest of them harder to find.
But when you do find a heavy metal like gold or silver, you will find a lot of it concentrated in the area of original discovery. That’s one reason the west had a gold rush, but has anyone heard of a head east young man, gold was found?
It was just the luck of the draw where the gold from one or more exploding stars wound up. Yes, our metals are most-likely the product of several exploding Supernovae.
There is no way anyone will tell you, looking at a current map of minerals on Earth, that the same locations will hold the same minerals. Many factors determine how much, if any, of the metal is even found on Earth.
For example, nickel is natural to Earth, yet most of it is deep inside the Earth. Because it is in many asteroids in our solar system, it is the 5th most abundant element in the Universe, but when found on Earth's crust, it's from asteroid impacts after the Earth cooled.
A planet even has a chance to not have any gold in it at all! Take the Moon. While there is gold and silver on the Moon, it has only been detected recently in the ice of the South Pole. Earth is devoid of Helium 3. Yet our Moon, which came from Earth, is loaded with Helium 3. Why? Luck of the draw? Helium 3 comes from the solar winds, which our magnetic field prevents helium 3 from reaching us.
If you are looking for a scientific approach, there is no secret formula that says an Earth-like planet will have 10 percent gold, 20 percent silver, 80 percent copper, etc. It does not work like that.
The planet Mercury has a lot of iron, the beneficiary of the Sun’s gravity. You would think that heavier metals would be gravitationally attracted to the Sun.
Even after all the minerals and metals have been placed on the Earth during its formation from both gathering material from the dust of the accretion disk and bombardments by comets and asteroids, water and wind and other forces over time moves these around.
As I said earlier, far more heavier metals made it towards the center of the Earth, but from water to lava flows to plate tectonics, minerals can concentrate around geographic features.
Like a miner who looks for quartz to find silver. When you map out your world, you also need to take into consideration these geographic features. For even if the Earth did not receive a certain metal or mineral, chemical reactions can create them over time, like turning carbon into diamonds.
Good luck. Placement of metals, removing the laws of physics such as gravity and amounts produced in the Universe, is a crap shot. But make sure that if you place gold or silver or copper that you also place its corresponding geographical features along with it.