Etiquettes

Using the left hand placing the right hand under the glass when drinking water

Q: While eating, right hand gets greasy, etc. Then most people feel dirty to take the glass with the right hand. Instead they would take it with left hand and right hand would assist by putting their hand under the glass. However, I feel that is just feeble excuse but we should still use right hand to drink. After all, we will wash the glasses anyway. Which is right way?