As usual, if various commodities find their way in the distant places, it is usually due to trade. Tobacco quickly found its way around the world, being primarily presented by Spanish merchants and Jesuit missionaries as early as 1530s. It is possible that the existence of tobacco and the custom of smoking it has been observed by Columbus during the first contacts, so the export could have begun with the subsequent expedition in early 1500s. Persian poet Muhammad ibn Yusuf Ahli Shirazi (c. 1454-1535) in one of his late poems mentions usage of 'galyan', which is a word used to denote a water pipe in farsi, although it is not sure whether such devices were already used to smoke tobacco or could have serve to smoke cannabis according to the Indian custom. Speaking of India, tobacco was also introduced there by Jesuits during the reign of Akbar the Great (reigned 1556-1605).
Tobacco was rather widely used in England in early 1600s, as James I was known to increase steadily increase taxes for this commodity in the first years of his reign, and in 1620 he issued a decree, according to which tobacco could have been traded only by the merchants possessing a royal patent. It is worth noting that James I was not fond of tobacco and even published in 1603 a brochure titled Misocapnus seu de abusu Tobacci iusus regius (Enemy of smoke or royal instruction concerning abuse of tobacco) where he claims that inhalation of tobacco smoke is detrimental to one's health and might cause a person to lose control over that pastime. Although widely criticized by Jesuits (mostly Spanish, and thus supporting one of the main exporters of tobacco) or Sigismund III Vasa, king of Poland (the latter even ordered in 1618 to publish a pamphlet titled Antimisocapnus critisizing James I and his anti-tobacco policies) it remains one of the first treatises rationally describing unhealthy and habit-forming properties of tobacco.
It is not really sure whether tobacco has been introduced to Russia and Polish-Lithuanian Commonwealth by the Turkish or English merchants. It is possible that tobacco leaves were included among the gifts Ottoman sultan Murad III sent to Polish king Stephen Bathory in 1577. Although somewhat corroborated by the linguistic evidence (Polish and Ruthenian words for tobacco are 'tytoń' and 'тютюн', respectively, most likely derived from Turkish 'tütün', while a pipe stem is called 'cybuch' and 'чубук' from Turkish 'cubuk' meaning 'pipe'), some historians suggest that tobacco was popularized by English, Scottish or Spanish merchants and pointing to the fact that in 17th century Poland and in Russia until this day, tobacco was called 'tabak' (according to them, Turkish terminology became popular only from the late 17th century onward, with the proliferation of the Oriental trade). Additionally, both Russia and Polish-Lithuanian Commonwealth had good commercial ties with England since mid-16th century, being main exporters of hemp, pitch and timber crucial to shipbuilding (Poland was also a major exporter of grain). If memory serves, during the reign of Henry VIII more than half of hemp used for sails was imported from Russia. This makes popularization of the tobacco in first decades of 17th century very plausible.
The theory of the Western route of tobacco propagation is also supported by rather restrictive measures taken by Ottomans against tobacco smoking in the early 17th century. Aforementioned Murad III (reigned 1574-1595) and Ahmed I (reigned 1603-1617) heavily restricted tobacco smoking and Murad IV (reigned 1623-1640) banned the consumption of tobacco, alcohol and coffee under the penalty of death. By that time, smoking was already popular pastime among common people in Central and Eastern Europe, with local rulers becoming more concerned with the fire hazard associated with it rather than smoking in general. For example, after the fire that broke in Moscow in 1634, tzar Michael I banned smoking in Russia (the ban, enforced primarily in cities, has been subsequently lifted by Peter I in 1697) and in 1637 Bogusław Leszczyński, owner of the Polish city of Leszno forbade smoking in the streets, backyards and attics within city walls. In mid-17th century smoking must have been very popular among all strata of Polish society, as the satirical poem published in 1650 stated that 'all peasants and even beggars always have some tobacco or snuff on them even when they have nothing to eat'.