Learn Russian: Раньше моя бабушка была медсестрой.

In Russian, when you talk about what someone's profession was in the past using the verb быть (to be), the profession goes into the Instrumental case. Since медсестра is a feminine noun ending in -а, it changes to -ой in the Instrumental case.

There is no verb for 'used to' here. How does Russian express this?

English often uses 'used to' for past habits or states. Russian simply uses the past tense of the verb, which in this case is была (was), combined with a time word like раньше. Раньше literally means 'earlier' or 'in the past'.

Why do we use была here?

Была is the feminine past tense form of быть (to be). It must match the gender of the subject of the sentence, which is бабушка (grandmother), a feminine noun.

Is the word медсестра made up of two different words?

Yes! It is a shortened combination of медицинская (medical) and сестра (sister). In Russian, a female nurse is literally called a 'medical sister'.