Okay, so the substances I'd concentrate on would be opium and marijuana/bhang/hashish (I know nothing about pre-Columbian America, maybe someone else could say something about tobacco).

Vedas mention usage of soma (mysterious herb or mix of herbs) and bhang - basically marijuana. It's one of the most basic written sources for Indo-Aryan civilization. However, soma and bhang were usually drank in a liquid form. That doesn't mean that they didn't inhale them - but I didn't find anything to support this idea, that's just my assumption.

The only source mentioning inhalations I've found is this: http://www.opiumpoppies.org/2001/07/13/the-early-history-of-the-poppy-and-opium/ In this article authors mention "opium inhalations" few times:

Diagoras[28] (third century B.C.), the commentator on Hippocrates, states that Epistratos, one of the founders of the Alexandrian School (304-257 B.C.), disapproved of the use of opium for ear-ache and eye ailments, because it "dulled the sight and is a narcotic", whereas Mnisidemos considered that the only proper use of opium was "by inhalation for inducing sleep, all other uses being harmful". Dioskourides adds that experience proves this to be untrue.

He [S.Mariantos] expressed the opinion that a tubular vase discovered at the same site, and belonging, according to S. Marinatos [55] , to the equipment of the goddess, was used for preparing inhalations of opium. This receptacle had a base and a hole on the sides, and bore a remarkable resemblance to those used in Java in earlier times for the inhalation of the vapours of opium [56] (Fig. 2).

From the other objects found near the goddess (receptacles and coals), it must be inferred that the opium was taken by the inhalation of vapours.

We must note with especial emphasis the original peculiarity of the censers, commented upon by Professor Marinatos,[63] and other objects in the Herakleion Museum yielded by excavations in Crete, which from the nature of their workmanship may be assumed to have been used for taking opium by nasal inhalation.

And last quote, which will get us an idea when they used mentioned object for inhalations:

in a grave at Pachyammos in the district of Hierapetra, was found jar, shown in Fig. 4, of the Late Minoan III period (1300-1250 B.C.). On the body of the jar the poppy head is portrayed between the sacred horns and is guarded by birds.

If they had a special object for inhalations, that means that smoking opium was a well estabilished practice. Moreover, I've read that traces of poppy seed usage date even to Neolithic period. As far as I know (or, in other words, what a drug dealer/restauranteur in Vang Vieng, Laos told me) the most potent way to use opium, is by inhalation (and no, I did not use opium, I prefer whisky).

While I can't positively say it's the first known evidence of smoking, one of the earliest mentions of smoking cannabis is in The Histories, by Herodotus, written around 450 B.C (he's describing the funeral rites of a people known as the Scythians):

After a burial, the Scythians go through a process of cleaning themselves; they wash their heads with soap, and their bodies in a vapor-bath, the nature of which I will describe.

On a framework of three sticks, meeting at the top, they stretch pieces of woolen cloth, taking care to get the joins as perfect as they can, and inside this little tent they put a dish with red-hot stones in it.

Now, hemp grows in Scythia, a plant resembling flax, but much coarser and taller. It grows wild as well as under cultivation, and the Thracians make clothes from it very like linen ones - indeed, one must have experience in these matters to distinguish the two, and anybody who has ever seen a piece of cloth made from hemp, will suppose it to be of linen.

They take some hemp seed, creep into the tent, and throw the seed on to the hot stones. At once, it begins to smoke, giving off a vapor unsurpassed by any vapor-bath one could find in Greece. The Scythians enjoy it so much that they howl with pleasure.

Sounds like a good time to me :)

By the way, Scythia was located roughly from the northern shore of the Black sea, stretching eastwards past the Caspian sea and covering a large amount of the so-called Pontic steppe. This area roughly includes the modern day countries of the Ukraine and Kazakhstan, and a large portion of central Russia.

The theory on the smoking of tobacco is that when forests were cleared by burning, the smell of the tobacco plant would have been interesting and studied closer. It originated in Equador and was spread throughout Mesoamerica.

Shamans would make a 3 foot long "cigar" and smoke until the point of nicotine poisoning, believing that this near death experience would take you on a spiritual journey. While no one knows exactly how far back this practice goes, it is obviously ancient in origin.

An interesting note from when the first Europeans smoked, Sir Walter Raleigh brought home tobacco and the first time his butler saw him smoking he poured water on him, believing he was on fire. In Elizabethan England, you would have servants carry your pipe and instruments, including the coal which they would light your pipe with.

Source: "Tobacco: A Cultural History of How an Exotic Plant Seduced Civilization" by Iain Gately

Maybe try asking /r/AskAnthropology, they may have something to say on it too!