Learn Dutch: Ik ga naar de dokter. - I am going to the doctor.

English uses the continuous "am doing" form a lot, but Dutch usually sticks to the simple present tense. So Ik ga can mean both "I go" and "I am going".

Why use the preposition naar here for "to"?

When you are expressing physical movement or travel toward a destination (like a place, a city, or a person), you almost always use the preposition naar.

How would I add an om ... te (in order to) clause to this sentence to explain why I'm going?

You can easily attach a purpose clause to the end! For example: Ik ga naar de dokter om een recept te halen (I am going to the doctor to get a prescription). Notice how om starts the extra information, and te halen goes at the very end of the sentence.

Is dokter the most common word to use, or should I use arts?

Dokter is the standard, everyday word used just like in English. Both are fine, though when referring to their local family doctor or general practitioner, Dutch people very often use the specific word huisarts.