Urination is the process by which urine is disposed from the body through the urethra, in humanoids as well as certain other creatures. To pee or to "take a leak" are slangs originating from Earth referring to the act of urination.
Zefram Cochrane conspired to escape the uncomfortable circumstances by stating that he had to take a leak as a ruse. Confused, Geordi La Forge stated that he couldn't detect a leak with his ocular implants. Cochrane explained that to take a leak meant to eliminate or pee. (Star Trek: First Contact)
In 2152, a minor diplomatic incident was caused when Porthos, the pet dog of Captain Jonathan Archer, urinated on the sacred trees of the Kreetassan people. While Archer had, in annoyance, mentioned the idea of urinating on these trees himself, due to the negligence of the Kreetassans to ensure Porthos's safety to pathogens in their atmosphere, the issue was resolved after Archer performed a Kreetassan apology ritual (ENT: "A Night in Sickbay").
The script of Star Trek, the police officer that chases young Kirk in Iowa first notices Kirk as he passes him while the officer is taking a "roadside piss". This is not shown in the film, where the officer is already in persuit on his hovercruiser when we first see him.
Among non-canon Star Trek publications, one of the more unusual topics brought up in the Star Fleet Medical Reference Manual is that Vulcan physiology naturally recycles their bodily fluids so much (to save water, living on a desert world) that their urine is thick and crude oil-black.