את is because
-THE beer has the definite
-beer is the object of the action 'give' me the beer.
ha beera - הבירה
בבקשה - bevakasha
carter, Though it's been a while for me, I do recall sound generally, obviously not for this one. I completely agree that "it's really hard to guess what words will sound like when most vowels" ( diacritic marks, vowel points, [NIKUDOT] ) are lacking! ...That's how I once learned [ :( ] ... :)))
First of all, i think את here is Et not At (as in feminine version of you אתה).
But then again, i find this sentence confusing too because it has no verb, so i guess the closest explanation is the one yonsub provides: that this sentence is actually a shortened version of a longer sentence like "(pass me) the beer, please". I tried to google translate'd it and the result is "תעביר את הבירה, בבקשה."
Assuming this is the correct situation so the verb תעביר is omitted here and probably substituted with some hand gestures or smthing like that