Learn Turkish: Doğru sayıyı bul. - Find the correct number.

This is the accusative case, which marks a specific direct object. Because you are finding a specific thing (the correct number), sayı (number) needs this ending. Since sayı ends in a vowel, we add the buffer letter -y- followed by the accusative vowel -ı.

If sayı gets an ending, why doesn't the adjective doğru get one too?

In Turkish, adjectives never change their endings to match the noun they are describing. The case ending only goes on the noun itself, which is why we say doğru sayıyı and not doğruyu sayıyı.

Why is the verb just bul instead of having a tense ending like buluyorsun?

This is a command (the imperative form). In Turkish, when you give an order to a single person you are informal with, you just use the bare root of the verb. The dictionary form is bulmak (to find), so dropping -mak gives you the command bul (find!).

I've also seen doğru used to mean "straight". How do I know which meaning it has here?

Context is key! Doğru is a very common word that can mean "correct", "true", or "straight" (like going straight ahead). Since a number can't physically be straight, it must mean "the correct number" in this sentence.