"I also want a glass of water."

Translation: Επίσης, εγώ θέλω ένα ποτήρι νερό.

[_Dimitris_]

Why not "Θέλω και ένα ποτήρι νερό";

[jaye16]

Yes, you're right I've added it thank you.

[Tato_Huenupi]

Why not Θέλω επίσης ένα ποτήρι του νερού?

[troll1995]

Ποτήρι του νερού means "water glass" ie a glass used for drinking water, not a glass with water in it, necessarily.