Learn German: Die Frau ist hier.

Die is the definite article ('the') used for grammatically feminine nouns that are the subject of the sentence (the nominative case). Since Frau means 'woman', it is naturally a feminine noun, so we must use die.

Why do we use the verb form ist?

ist means 'is' and is a form of the irregular verb sein (to be). We use it here because the subject, Die Frau, is a third-person singular noun. It works just like English: 'I am' (ich bin) but 'she is' (sie ist).

If I wanted to replace Die Frau with a pronoun, which one would I use?

You would use sie, which means 'she'. Because Frau is a feminine noun, you refer to it with the feminine pronoun. If you swap out the noun phrase, the sentence becomes Sie ist hier (She is here).

Why is Frau capitalized?

In German, every single noun (a person, place, thing, or idea) is always capitalized, no matter where it is placed in the sentence. Since Frau (woman) is a noun, it must be written with a capital letter.