Puedes: * Llenar un vaso con agua/Verter agua en el vaso. (Pour) * Rellenar el vaso con agua. (Refill) * Servir un vaso con agua. (When you simply ask for a glass of water) "Estaba llenando/rellenando un vaso con agua."

Puedes decir: llenar el vaso de agua (to fill) verter agua (to pour) no muy usado echar agua a... rellenar (refill) if its the second time you fill it.

when I am getting water for someone or asking if they would like me to "basically put water in their glass", I would say, "Would you like me to pour you some water?". I might say "Do you want me to fill it? Do you want me to fill it all the way up?" Or, I might ask, "Do you want me to pour you half a glass of water?" In regular conversation, it won't matter so much, but it may matter if you are taking a test.