Learn Spanish (Spain): A veces me duele la cabeza.

It doesn't have to! Adverbs of frequency like a veces (sometimes) are quite flexible in Spanish. Putting it at the beginning is very common and sounds natural, but you could perfectly well say Me duele la cabeza a veces.

Why is it me duele? How does this verb work?

The verb doler (to hurt or to ache) works exactly like gustar. Literally, this sentence translates to "Sometimes the head hurts to me." The pronoun me tells us who is feeling the pain, and duele means "it hurts."

Why does the sentence use la cabeza (the head) instead of mi cabeza (my head)?

When talking about body parts or clothing, Spanish uses definite articles (el, la, los, las) rather than possessive words like mi (my). The pronoun me earlier in the sentence already makes it perfectly clear whose head is hurting.

What if more than one thing hurts? Does duele change?

Yes! Because the body part is the actual subject of the sentence, the verb has to match it. If your legs hurt, you use the plural form duelen and say A veces me duelen las piernas.