There is reference to the spells being created, but only after they are in existence, nothing about how to create them (Other than crossed out versions in the margins of the book, thanks to @mithrandir).
From The Half Blood Prince:
“Sectum — !”
Snape flicked his wand and the curse was repelled yet again; but Harry was mere feet away now and he could see Snape’s face clearly at last: He was no longer sneering or jeering; the blazing flames showed a face full of rage. Mustering all his powers of concentration, Harry thought, Levi —
“No, Potter!” [...] Snape’s pale face, illuminated by the flaming cabin, was suffused with hatred just as it had been before he had cursed Dumbledore.
“You dare use my own spells against me, Potter? It was I who invented them — I, the Half-Blood Prince! And you’d turn my inventions on me, like your filthy father, would you? I don’t think so . . . no!”
As evidenced, Levicorpus and Sectumsempra are inventions of Severus. The names are in fact descriptions of what the spell does, as the Latin levitas and corpus translate to levitate body (And the counter spell liberacorpus, libera = free), and sectum (to cut), sempra (permanently/always).
Also, existing magic can be improved, also as evidenced by Snape improving the textbook instructions (Still in use 40+ years later) on how to make potions.