If I were doing it, I'd bring a soup plate, carefully slide the glass to the edge of the table, and pour the water into the soup plate. The water wouldn't spill on the floor.
Literal
I [if-なら] soup-plate [object-を] bring-come-and, glass [object-を] sufficiently cautious-while table [of-の] edge [until-まで] slide-and water [object-を] that soup-plate [into-に] pour-into [reflective-な]. Water [topic-は] floor [onto-には] not-spill.
An elaborate hypothetical with extensive te-form chaining. 僕なら ('if [it were] me') sets the hypothetical. ながら ('while') joins 注意する to 滑らせる. 滑らせる is the causative of 滑る ('slide') — 'make [glass] slide.' 流し込む is a compound: 流す ('pour, flow') + 込む ('go inward') = 'pour into.' The ending な marks reflective musing. The second sentence is a simple confident prediction. A demonstration of Japanese's capacity for long chained narratives.