Learn Spanish (Spain): Tengo que ir al médico mañana. - I have to go to the doctor tomorrow.

In Spanish, when you want to express an obligation like "I have to" do something, you must use the special phrase tener que followed by an unconjugated verb (here, ir). If you just said tengo ir, it would sound as incorrect as saying "I have go" in English.

What exactly is the word "al"?

The word al is a mandatory contraction of the preposition a (to) and the masculine word for "the", which is el. Whenever a is followed immediately by el, they always merge into al to make pronunciation smoother. You are literally saying "to the".

Does "mañana" mean "tomorrow" or "morning" in this sentence?

Here it means "tomorrow". The word mañana is tricky because it can mean either "tomorrow" or "morning" depending on the context. If you wanted to specify that you were going "in the morning" rather than just tomorrow, you would use the phrase por la mañana.

How would this sentence change if my doctor is a woman?

If you are referring to a specific female doctor, the noun changes to médica. Because the feminine word for "the" is la, and a does not merge with la like it does with el, the sentence becomes Tengo que ir a la médica mañana.