The best way to understand べし is to look at how it was used in classical Japanese, because some of that usage extends into modern Japanese. Then, separately look at how it is used commonly in modern Japanese.
Etymologically, べし probably came from the adjective うべし as Tsuyoshi Ito said, just shortened for use as an auxiliary adjective, and additional meanings/usages were added to it over time.
べし attaches to the 終止形 or 連体形(ラ変). In modern Japanese, the distinction between 終止形 and 連体形 has deteriorated, but in classical Japanese, for instance, this would mean 食ぶべし rather than 食ぶるべし, すべし instead of するべし, あるべし instead of ありべし. - As a given rule there is always an "u" sound before the べし.
The classical conjugation for べし is like all classical ク形容詞, (べから・べく、べかり・べし・べき、べかる・べけれ、べかれ）.
However in modern Japanese べき basically transformed into a restricted な adjective. Or, if you don't want to call it that, a 終止形 form べき(だ)、and 連体形 form for use with particles べき(なの), that are like the corresponding な conjugations were added to the list of possible べき forms in modern Japanese. Other strange and restricted な adjectives that used to be 形容詞 include 同じ (mix of original and な-adj ish form) and 大し→大きな (連体形only).
These conjugations mix together in modern Japanese, using the classical for phrases like ～べからず, ～べからざる, すべき - and modern for するべき, ～べきだ.
Anyway, the best way to understand is studying on your own. 頑張ってください。
Knowing the etymology is very helpful to understanding sometimes, but you have to remember that it isn't always everything.
You could think of しかし in terms of of しかじ (classical form), which is just a conjugation of the verb 如く, which is the basis for a whole slew of other things, and give yourself a headache, or you could just pay attention to how and where it is used regularly in sentences.