When did advertisements first start being used? Are they a relatively recent phenomenon (as in within the last 200 years), or are there older examples of advertisements?

The answer changes wildly depending on what you mean by "advertisements."

-do you mean simply using some form of communication to promote your wares?

-do you mean commercial messaging crafted and spread by paid professionals who have some expertise or even training?

-or do you mean an entire economic and cultural system of late capitalism that uses feedback loops of modern communication technologies to increase consumption by reshaping people's very identities?

Most of the first "histories of advertising" written in the late 19th century (say, in the 1880s or 1890s) claimed that advertising was 'ancient', stretching all the way back to the first time that a fishmonger shouted out "fish for sale!" (Like Henry Sampson's History of Advertising from 1874.) This was a way for these authors--most of whom came from this new class of professional in the 1880s, the professional "advertiser"--to claim that their profession was not sketchy at all, but rather stretched all the way back to the dawn to time. This is not really useful, though.

If "advertising" is nothing more than speech used to facilitate trade something to someone for something, that can it really usefully be separated out from speech at all? (trade, in fact, probably predates language...but that's another matter.)

Most importantly, we lose the sense of advertising's historicity--it's historical uniqueness--if we lump it into any speech or writing that happens to facilitate trade.

Yes, there are carved store signs going back to Ancient Egypt (2000 BC), and hawkers and sellers have used speech and writing to help sell their wares. But there has been a HUGE transformation, that had its roots about 200 years ago, but really took off 100 years ago, which has profoundly changed, well, everything.

So, instead, I find it best to break "advertising" into three stages: mercantile notices (starting around 1700); professional agencies (starting around 1860); and universal appeals (starting around 1890).

"mercantile notices" arose with the first means to 'broadcast' a sales message widely... namely, print.
While the first uses to which the printing press (after 1450) were put were for religion (Reformation and Counter-Reformation) and pornography, it also ultimately became a useful way to transmit news--and commercialize that transmission. News was first mostly useful to merchants, but as more people paid for news broadsheets, they became more widely available, and people (especially of the emerging middle class) became more accustomed to wanting news. So, by the end of the 17th century, news sheets were on the rise, and everywhere by the 18th century.

Yet, in the days of typographic print, once all of the (known) news was typeset, there was often 'left over' space. So, clever news-sellers started allowing merchants to pay a small fee to add in a commercial "news" message: "Jannsen now has cigars for sale on 14 Halfpenny Lane". This was the origin of the classified ad.

So far so good. Newspapers expanded in size, because more news became interesting to a broader readership (still upper- and middle-class though), paper (originally made from rags) became slightly cheaper, and the fees for merchant's classified 'notices' helped to subsidize the whole newspaper to make it even cheaper and so, more widely-affordable.

Eventually, the classifieds became as important as the subscribers or street purchasers for financially supporting the paper.

Some of these printers started offering 'extras' to merchants (for extra money, of course) to attract more attention to their classified. These were usually graphics of some sort--thicker lines to "frame" the classified, or drop-in black pointing hands. Some also inserted pre-carved woodcuts to "illustrate" the product... but these were re-used for different things. (A black figure for a tobacconists might represent a cigar-store Indian, while the same figure might also be used to illustrate the sale of slaves.)

By the 1850s, classified sections had expanded, and were utterly necessary to newspapers... but for merchants, they were getting 'crowded'. (i.e. it was hard to 'see' a specific merchant's classified in three pages of dense text.) And there were a huge number of different newspapers.

professional advertising

So, professional "brokers" of classifieds emerged. At first, all these brokers did was to act as middlemen--you (a merchant) would go to them with your money, and for a set price they would place your classified in the 3 (or 6 or 12) most relevant papers. Then they started (for a fee) offering extra advice on crafting your text message, and whether to pay extra for an engraved illustration.

By the 1880s, these had developed into large, multi-person operations. Most of these early 'advertisers' were considered pretty sketchy... just a step up from the patent-tonic salesmen. And so they sought to 'gentrify' themselves a bit, by trying to assert their professionalism and their importance to society as facilitators of commercial communication. (T. Jackson Lears' old but famous article "From Salvation to Self-Realization" is pretty great distillation of this process.)

And by the 1930s, there emerged professional trade-schools that actually taught "advertising" (and it's related fields, like graphic design.)

The New Universe of Advertising

But the huge revolution in advertising was not about professionalization, but about new technology. Namely, it followed the massive advances in printing in the 1880s and 1890s--twin rotation press (for cheap printing), cheap chromolithography (for posters and product packaging), and so on.

Basically, illustrations became a lot cheaper, and that meant they became available for advertising. Which changed the whole game, as now it wasn't just about classifieds in a newspaper, but about colorful posters on walls, packaging items in chromolithographed tins, or wrapping 'bulk' goods like soap in lithographed paper or cardboard packaging. (Modern packaging was first and foremost about advertising, less about 'preservation.')

With this printing revolution, commodities--which had formerly been sold in bulk--or products could now be 'branded.' (good books on this are Ohmann, Selling Culture and Paul Messaris, Visual Persuasion for the USA, Thomas Richards, Commodity Culture of Victorian England, and David Ciarlo, Advertising Empire for Europe)

Certain types of manufacturers (soap, cigarettes, etc.) pioneered this branding process. Pears Soap was in particular at the forefront of this new approach to advertising.

And images, by the way, had a much wider appeal than classifieds... they could appeal even to the semi-literate (i.e. cross-class appeal) and they could 'escape' newspapers by appearing on posters and packaging.

By 1900, images were 'branding' products.

By 1930, 'lifestyle' advertising had emerged, using images to associate a style of life with the brand. (implying you could attain that style by purchasing that brand.)

By the 1960s, television advertising made this sort of lifestyle advertising truly universal in reach and appeal.

Advertising is now the single most important 'force' in modern world history, I would argue, even though it is created by scattered and diffuse producers.

Because, by altering what we see (and how we see it), it shapes our identities in ways that we have little or no awareness of.

Sources:

Susan Strasser, Satisfaction Guaranteed

Ohmann, Selling Culture

Thomas Richards, Commodity Culture of Victorian England

Richard Ohmann, Selling Culture

T Jackson Lears, Fables of Abundance

David Ciarlo, Advertising Empire

Anandi Ramamurthy, Imperial Persuaders

Stephen Eskilson, Graphic Design: A New History