A lot of recreational drug slang is reasonably comprehensible. Some is pretty cryptic, possibly by design. A common expression for "take LSD" is "drop acid". The "acid" part is obvious; it's a common expression for lysergic acid diethylamide. But whence "drop"?
Green's Dictionary of Slang links all uses of drop related to drugs under one definition.
v.6. 1. (drugs) to consume pills or any drug that can be taken orally.
The earliest cited use is from 1961:
The drugs are either inhaled, swallowed or injected [...] To take orally is to ‘drop it’.
- 1961 - The Real Bohemia by Francis J. Rigney and L. Douglas Smith. New York
It's possible that the word "drop" grew in association with LSD because of the well-known counter-cultural mantra coined by Timothy Leary:
Turn on, tune in, drop out
Wikipedia quotes Leary describing the meaning of drop out in this phrase:
"Drop Out" meant self-reliance, a discovery of one's singularity, a commitment to mobility, choice, and change. Unhappily my explanations of this sequence of personal development were often misinterpreted to mean "Get stoned and abandon all constructive activity".
So it is clear that "drop out" in the phrase was not meant to refer to the act of taking LSD, but Leary's reputation as a popularizer and proponent of LSD use might have led to misinterpretations of "drop out" referring either to dropping away from social awareness or, possibly, "dropping acid."
I think it's fairly obvious. From a transitive sense of drop, "to let fall (like a drop or drops)," the OED gives
c. To swallow or take (a drug); esp. in phr. to drop acid (cf. acid adj. and n. Compounds 2). slang.
1966 R. Alpert & S. Cohen LSD (inside cover) Drop a cap, swallow a capsule of LSD.
1967 R. Bronsteen Hippies' Handbk. 13 I dropped my first acid in Paris.
1969 Guardian 3 Dec. 9/1 She had dropped some LSD and had been tripping for an unknown number of hours.
1971 ‘E. McBain’ Hail, Hail, Gang's all Here ii. 170 I realized he was on an acid trip... I tried to find out what he'd dropped.
1973 M. Amis Rachel Papers 183 I was using the Mandrax my dentist had given me, surreptitiously dropping one at ten thirty.
1984 S. Bellow in Vanity Fair (N.Y.) Feb. 110/2 Some kids are dropping acid, stealing cars.
1985 S. Vanauken Under Mercy iv. 81 We obtained two six-hit caps and, recklessly, decided to drop the lot.
When I was young it was always understood that to drop a pill (or a liquid drop of a drug) meant to swallow it.