Learn Spanish (Latin America): Yo doy una clase en la mañana.

Doy comes from the verb dar (to give). It is one of a few verbs that have an irregular yo (I) form in the present tense. Instead of dropping the ending and adding -o (which would be "do"), it takes the irregular ending -oy. Another common verb you have seen do this is estar (to be), which becomes estoy.

Does dar una clase mean I'm teaching the class or attending it?

It means you are teaching it! Just like in English, "giving" a class (dar una clase) implies you are the instructor. If you were a student taking the class, you would use the verb tomar (to take) and say tomar una clase.

Do I have to include Yo at the beginning of the sentence?

No, it is completely optional. Because the verb form doy can only ever mean "I give," the pronoun yo isn't strictly necessary. You could simply say Doy una clase en la mañana. Speakers often include yo to add emphasis.

Why is it una clase? Doesn't clase end in "-e" instead of "-a"?