Tobacco:

You may be interested in these two answers I have written in this sub before: this thread answers the question about how Europeans were introduced to tobacco, and this thread answers the question about how soon Europeans suspected smoking tobacco had adverse health effects. In that second thread, /u/bodombeachbod provides some additional info, too. In short, Christopher Columbus and crew encountered tobacco as a gift pretty much the moment they landed in the New World, and before they left months later, there was evidence that some of the crew had become addicted. The health effects were pretty apparent to the Europeans early on, and by 1600, there were several different people who had written against tobacco as unhealthy, including King James I of England.

In this thread, /u/Reedstilt goes into some of the prehistory of tobacco use by Native Americans before European contact, but since there isn't really anything as far as written records go, it goes outside the realm of history and starts talking anthropology. In that same answer, /u/Reedstilt addresses the question of cannabis use by Native Americans--and that answer is, there wasn't any because cannabis was introduced from the Old World to the New World.

This scholarly journal estimates that smoking tobacco in North America goes back to at least the 800s C.E. in the Pacific Northwest, as estimated through anthropological evidence, while this paper says that it dates to 1000-2000 years ago in Eastern North America, according to radiocarbon dating estimates. In South America, physical evidence from Peru dates tobacco use even earlier, to about 1000 B.C.E., though that evidence is of snuffing tobacco rather than smoking it, so it's likely that much of the New World first started smoking rolled tobacco somewhere between 3000 and 1000 years ago.

Cannabis:

This answer provided by /u/Yearsnowlost is linked in this sub's FAQ and thoroughly covers the subject of the early history of smoking cannabis. Cannabis use dates to prehistoric times, with the earliest written evidence in China and India.

This scholarly journal article pinpoints the first written reference to marijuana to be from 2737 B.C.E. by Chinese emperor Shen-Nung. The article then gives a further rundown of early marijuana cultivation, and references the book Man and Marijuana: Some Aspects of their Ancient Relationship by Mark David Merlin as a source for the infromation about Shen-Nung.

This article entitled "Physical Evidence for the Antiquity of Cannabis Sativa" from the Journal of the International Hemp Association gives a more lengthy anthropological rundown of the evidence for cannabis cultivation in the Old World. The earliest evidence cited is of some carbon-dated hemp rope found at an anthropological dig in the Czech Republic, and first written about by Heather Pringle in her article "Ice Age Communities May Be Earliest Known Net Hunters" published in Science magazine in 1997. The conclusion is that humans have been using the cannabis plant for some 27,000 years.

Opium:

Last but not least, this book about opium gives a brief history of the drug's ancient use, and gives some sources. The earliest written historical evidence comes from the Sumerians in approximately 3400 B.C.E. where it was called "hul gil", meaning "joy plant". Another source backing this up can be found here, and a more scholarly article on the history of opium can be found here though it's behind a paywall.

Who? How? Why?:

These questions can't really be answered from an historical standpoint, since history deals with written evidence, rather than with anthropological or archaeological evidence. So we can say who first wrote about these things (the Chinese first wrote about cannabis, the Sumerians first wrote about opium, and the Europeans first wrote about tobacco when they made contact with the New World), but we can't say who exactly the first person to smoke is. And because of that, we can only make educated guesses as to how and why. The how is pretty easy--there is physical evidence of different pipes, made out of clay and such materials, dating to prehistory, and smoked tobacco was rolled in tobacco leaves when Christopher Columbus first encountered it. But "why", we don't know, other than to say that at some point early on, there is evidence it was used in religious rituals, as is argued in Tobacco and Shamanism in South America by Johannes Wilbert.

In another thread when this question has been asked in this sub, /u/orthoxerox put it pretty succinctly, so I'll copy-paste that answer here:

Invention of smoking is prehistory, not history. No one will give you a definitive answer, that's like asking why people started drinking fermented juice.

People have burnt countless grasses and woods over the millenia of fire use. They could've used cannabis as tinder, they could've burned it to clear fields for crops or they could've experimented with aromatic grasses to keep insects away or improve the air quality of their dwelling.

In other words, through numerous human activities, humans discovered these plants, and stumbled on their psychoactive effects. From there, they became ritual and then habitual. But because it's all prehistory, we can't know for sure exactly what happened.

TL;DR: Tobacco use in the Americas goes back at least 3000 years, with tobacco smoking going back at least 1000-2000 years, maybe further, but there's no written evidence until European contact. Europeans encountered the drug as soon as they made contact with the New World in 1492. Marijuana cultivation goes back about 27,000 years according to anthropological evidence, with the written record going back about 5000 years. Opium use also goes back to prehistory, and the written record of its use also goes back about 5000 years. It was smoked in pipes and leaves, according to the earliest physical and written evidence, but we don't know why they started using them originally or how exactly they were discovered.

EDIT: Grammar.