Spruce beer is made from the tips of spruce trees. Except that the connection is not as simple as it appears: it is pretty much a coincidence that spruce beer and spruce trees have the same name.
There are actually two traditions of spruce beer in Britain: the older, the Danzig or Black Beer tradition, only died out very recently, while the other, which could be called the “North American tradition”, was hugely popular in Regency times, and included Jane Austen among its fans, but disappeared nearly 200 years ago on this side of the Atlantic.
The first mention of “spruce beer” in English is from around 1500, when Henry VII was on the throne, in a poem called Colyn Blowbolles Testament, in which a hung-over drunkard is persuaded to write his will. Colyn lists the drinks he wants served at his funeral, including more than a dozen types of wine, mead, “stronge ale bruen in fattes and in tonnes”, “Sengle bere, and othir that is dwobile”, and also “Spruce beer, and the beer of Hambur [Hamburg]/Whiche makyth oft tymes men to stambur.”
The fact that spruce beer and “the beer of Hambur[g]” were mentioned together is because both came from North Germany. The name “spruce beer” is an alteration of the German “Sprossen-bier”, literally “sprouts beer”, more meaningfully “leaf-bud beer”, since it was flavoured with the leaf-buds or new sprouts of Norway spruce, Picea abies, or silver fir, Abies alba. “Sprossen” was meaningless to English-speakers, but in early modern English the similar-sounding “Spruce” was another name for Prussia, from which country’s main port, Danzig, Sprossen-bier was exported. “Sprossen-bier” became in English the more understandable “Spruce beer”, meaning, originally, “Prussian beer”. (Chaucer called the country “Sprewse”, and it was being called “Spruce-land” as late as 1639.)
Meanwhile English had to wait more than a century and a half after the beer was named to get its own word for Picea abies, the tree known as Fichte in German and gran in Norwegian. When the tree did get an English name, first mentioned by the naturalist John Evelyn in 1670, because it, too, like the beer, came to Britain via Prussia, it was called the “Spruce”, short for “Spruce fir”, that is, “Prussian fir”. Thus “spruce beer” is not actually named for the spruce tree, and “spruce beer” in English is around 170 years older as a phrase than “spruce tree”. (The adjective “spruce” meaning “neat” or “smartly dressed” probably also comes from “Spruce” meaning Prussia, via “Spruce leather”, leather from Prussia that was a favourite, it appears, among Tudor dandies.)