"A glass of beer and a glass of wine, please."
Translation:Et glass øl og et glass vin, takk.
The most common way is to when you order something at a restaurant or bar is to add "takk" at the end "En øl, takk".
But you could also say: "En øl, er du snill". But it is not as common, and would probably be used more frequently at home or in social settings.
"Kunne du være så snill å gi meg en øl" would be comically polite and "En øl, vær så snill" would sound a bit desperate.