Learn Russian: Где белый кот?

In Russian, adjectives must match the gender of the noun they describe. Because кот (cat) is a masculine noun, the adjective takes the masculine singular ending -ый, making it белый.

Where is the word for "is" in this sentence?

Russian usually leaves out the verb "to be" in the present tense. So instead of saying "Where is the white cat?", you simply ask "Where white cat?" (Где белый кот?).

If I wanted to talk about a female cat (кошка), how would this sentence change?

You would need to change the adjective to its feminine form to match the noun. The feminine ending for this adjective is -ая, so the sentence would become Где белая кошка?.

Does the adjective always have to go before the noun?

In standard everyday Russian, yes. Adjectives usually go right before the noun they describe (белый кот), exactly like they do in English. Putting it after the noun is possible but usually sounds dramatic or poetic.