Learn Spanish (Latin America): Yo tengo mucha hambre.

In English, we describe physical states using "to be" plus an adjective (like "I am hungry" or "I am thirsty"). In Spanish, you use the verb tener (to have) plus a noun. So, you are literally saying "I have hunger."

If the translation says "very hungry", why doesn't the Spanish sentence use muy (very)?

Because hambre is a noun meaning "hunger," not an adjective. You can't say "I have very hunger" in English, and you can't say it in Spanish either! Instead, you use a form of mucho, which means "a lot of" or "much."

Why is it mucha ending in 'a', rather than mucho?

The word hambre is a feminine noun in Spanish. Because words that describe a noun must match its gender, the masculine word mucho changes to the feminine mucha.

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

No, it is completely optional. You can just say Tengo mucha hambre. Because the verb form tengo specifically means "I have," the listener already knows who you are talking about. Including Yo just adds a little extra emphasis.