"He gives me a cup of coffee."
Translation:Han ger mig en kopp kaffe.
I discussed this with my swedish collegue this week. I have a list with all the 'ett' words I know, so that I can remember them. When I showed it to her, she said that they say 'en kaffe' and not 'ett kaffe'. So I said: but you say 'det här kaffet är gott' right? We concluded that kaffe is an 'ett' word and that 'en kaffe' (and 'en te') are very common expressions and that they indeed come from 'en kopp kaffe' and 'en kopp te'.
I hope that helps all other people who were wondering the same thing!