Learn Turkish: Bu kız spor yapıyor. - This girl is doing sport.

You would change yapıyor to yapmıyor. The verb root is yap- (to do). To make it negative in the present continuous tense, you add a negative particle before -yor. Because of the 4-way vowel harmony with the 'a' in yap-, that particle is -mı.

Why doesn't the word spor have any endings attached to it?

When you talk about doing a general activity rather than acting on a specific object, Turkish leaves the noun bare. Spor yapmak (to do sport) acts like a set phrase. If you added a specific object ending like sporu, it would mean she is doing a very specific, previously mentioned sport.

Where does the ı in yapıyor come from if the verb root is just yap-?

The present continuous suffix is -yor. When a verb root ends in a consonant like yap-, it needs a helping vowel to connect to -yor. Because the vowel in yap- is an 'a', the 4-way vowel harmony rule dictates that we use ı, making it yapıyor.

If I wanted to say 'These girls are doing sport', would I change Bu to Bunlar?