Learn Russian: Врач — хорошая профессия.

In Russian, the present tense of the verb to be (like am, is, or are) is usually left out. When you are linking two nouns together to say one thing is another, like врач (doctor) and профессия (profession), you use a dash to show where the word is would go in English.

The word for doctor (врач) is masculine, so why is the word for good (хорошая) in the feminine form?

Adjectives must always match the gender of the noun they describe. In this sentence, хорошая is describing the word профессия (profession), which is feminine because it ends in -я. It is not describing the masculine word врач.

Is the word врач used for both male and female doctors?

Yes! Many Russian words for professions, like врач, are grammatically masculine but are used for people of any gender. If you want to say a woman is a doctor, you still use the word врач.

Why are there no words for 'a' or 'the' in the Russian sentence?

Russian does not have articles like 'a', 'an', or 'the'. You have to figure out from the context whether a sentence is talking about a specific person or a general concept. Because this is a broad statement about the job, translating it as 'A doctor' or just 'Doctor' makes the most sense in English.