The dates corresponding to the levels of the dig are older the farther down you go, this seems fairly simple. But wouldn’t that mean that mulitple layers of material have been added to the planet since way back when? Where did all of this new material come from?
It’s not that there have been universal layers of stuff deposited over the entire earth’s surface. It’s just that material is deposited in some places and blown or eroded away from others; in the latter you are naturally not going to get anything to dig up. So archaelogical sites are self-selecting to be in places where material gets deposited.
The other factor is mankind. We bring stuff in from the countryside and toss it away near the cities, in general, so there’s a greater chance of artifacts being buried as there are more around cities.
I read recently on an astronomical site (maybe the NASA astro pix of the day?? which usually changes every day, but they have an archive with a search engine [COLOR=DarkGreen]{not, IMO, a very good one; I’d Google if I really wanted to find it.})[/COLOR] that there are x many tons of space dust deposited per year on Earth. Makes sense to me. <shrug>
However: The way that archaeological sites build up is that people bring stuff into their campsites/houses/etc. Depending on where in the world you’re talking about, people would let trash build up inside their homes as recently as a hundred years ago. In Europe, that pretty much stopped around the time of the Renaissance, I think.
But if you are talking about a site in or around one of the centers where civilization goes back for thousands of years (e.g., Egypt, ancient Iraq, ancient Iran, China, India, couple of sites in South America), choice places to build your village (near running water and easily tillable fields) would be conquered by somebody else periodically. The flimsy dwellings (think hovels) would usually be demolished as part of the battle/looting/etc. The winners (whether the people who lived there or the attackers) just leveled what was left and built on top of it. In the Middle East, there are things that look like hills, and the Arabic word transliterates into English as “tell”. These “hills” are actually ancient village sites.
Does that answer your question, OP? 
<sigh> I should get in the habit of thinking of searching Cecil’s columns. It would probably save me the time it takes to write a response.
I learned some of what I know in (required) archaeo classes for the anthro major, but knew most of it from intermittent subscriptions over the years to Biblical Archaeological Review, which has scholarly articles, but is edited with the objective of remaining readable to the interested “(wo)man in the street.”
I might also point out that an exceedingly painless way of absorbing a great deal of factual background about archaeology and about societies which were at a level comparable to the Middle Ages from Harry Turtledove’s (he’s a Ph.D. in Byzantine history) fantasy books, particularly those set in the Videssos universe. AAMOF, the Videssos universe recasts the centuries-long struggle between Byzantine Christianity and Islam in the several series set in different eras of its “history”.
The space dust information, of course, comes from astronomy/space websites.
If you’re talking about the creation of the dirt itself that covers archaeological sites, you’ll have to go back virtually to the beginning of the earth. “New” material is being created all the time, and has been since the earth was formed. When those planetoids during the Big Bang stuck together and formed what would later be earth, they were really hot. The heavier, metallic elements moved toward the core of the new earth, while the lighter ones rose to the top and formed a kind of scum/crust on the surface of the planet. The earth was gradually covered by a vast ocean. As the earth reduced and cooled from the violent collision over several million years, volcanoes were exploding (called outgassing - they were releasing the lighter gases on the earth’s surface), and continents began to form. This was about 3 billion years ago (70% of the world’s continents were formed during this time period). So that’s the formation of most of the continents. That covers a lot of layers, because you have to keep in mind that the volcanoes creating these continents were started at the bottom of the ocean, and as they exploded, they continued laying down new layers of rock and ash. We still have lots of active volcanoes today, so they continue to deposit new layers on the earth. Some continents, like Hawaii, are still forming.
There are also things like space dust, and erosion, flooding which brings additional layers, etc., that add more layers to certain areas or take away layers from others. Keep in mind, though, that layers are by no means uniform all over the world. Some areas are more prone to erosion (such deserts, where the sand moves around easily), while other areas seem to collect layers (such as floodplains, which are often fairly low-lying and collect debris).
As for how archaeological sites get covered by the dirt and other stuff that’s already there, usually it was caused by man covering things up (such as shoveling dirt into rubbish pits, or “borrow” pits), or floods depositing lots of silt on sites too close to a body of water, or a site being covered by volcanic ash, or even a bog or swamp forming where a site used to be. Most natural site covering such as bog formation and erosion happens over time; floods, volcanoes, and people tend to bury things much faster.