Learn Polish: Dodałam trochę wody zamiast mleka, bo jestem na diecie. - I added a little water instead of milk, because I am on a diet.

The preposition zamiast (instead of) requires the noun that follows it to take the Genitive case. Since mleko is a neuter noun, its Genitive form is mleka.

Why is it wody instead of the Accusative wodę? Doesn't the verb add take a direct object?

You are right that direct objects usually take the Accusative case. However, the word trochę (a little) is a quantifier. In Polish, quantifiers override the verb and force the noun that follows them into the Genitive case. So, woda becomes wody.

How do we know the gender of the person speaking?

The past tense verb dodałam ends in -łam, which tells us the speaker is female. If a man were speaking, he would use the masculine ending and say dodałem.

Why does the word dieta change to diecie?

The phrase na diecie (on a diet) uses the preposition na to describe a state, which triggers the Locative case here. For feminine nouns ending in -ta, the Locative ending causes a consonant mutation where t softens to ci, making it diecie.