Learn Polish: Proszę pół kilograma mięsa. - Half a kilo of meat, please.

The word pół (half) expresses a quantity. In Polish, words expressing quantities make the noun that follows them take the Genitive case. Kilogram is a masculine inanimate noun, so its Genitive form is kilograma (half of a kilo).

Why is mięso (meat) also in the Genitive case as mięsa?

This is exactly like the English word 'of'. Whenever you are expressing a measure or container of something (like a bottle of water, or a kilo of meat), the substance being measured takes the Genitive case. Since mięso is a neuter noun ending in '-o', it changes to mięsa in the Genitive.

Does the word pół change depending on the gender of the noun it describes?

No, pół is super easy to use because it never changes form! Whether you are talking about a masculine noun like kilogram, a feminine noun like godzina (hour), or a neuter noun like jabłko (apple), you just use pół followed by the Genitive case of that noun.

I know proszę means 'please'. Why is it used at the start of the sentence instead of the end?

Proszę literally means 'I am asking for' or 'I request' (from the verb prosić). While we often translate it as 'please' in English, in Polish shops or restaurants it acts as the main verb of the sentence, meaning 'I would like...' or 'Please give me...'. That is why it stands at the beginning and doesn't need another verb next to it.