Learn Turkish: Bugün alışveriş yapıyorum.

In Turkish, many actions are expressed using a noun plus a helper verb like yapmak (to do/make). Alışveriş is the noun for "shopping" (literally "taking and giving"), so to say "to shop", you say alışveriş yapmak (to do shopping).

This lesson is about the negative suffix. How would I change this sentence to say "I am not shopping today"?

You would change the verb to yapmıyorum. To make the present continuous tense negative, you add the negative particle (in this case, -mı) right after the verb root yap and before the continuous suffix -yor. The full sentence becomes Bugün alışveriş yapmıyorum.

Why is there an ı between yap and yorum in the positive version of the verb?

The verb root is yap (do) and the present continuous suffix is -yor. Because yap ends in a consonant, we need a connecting vowel to stick them together. According to the rules of vowel harmony, the a in yap requires an ı, giving us yapıyor before we add the "I" ending -um.

Does the word bugün literally mean "this day"?