As in any sexual euphemism, the act of "sliding clyde" refers to the penetration of a female's erogenous zone(s) with the males erect member.
Despite this phrase acting as a verb, there is in fact a verb and a noun within. The verb being, slide. And the noun being, clyde. The name clyde is representative of said male member, just as the term Johnson, Dick, Willy, etc.
~Two male comrades, Chris and Jeremy, at a bar.
Jeremy: "Damn, those two are sure going at it."
(Jeremy is referencing two young heterosexual individuals engaging in excessive public foreplay)
Chris: "Oh yeah! I guarantee he'll slide clyde tonight."