Learn Portuguese (Portugal): Tenho muita sede.

In Portuguese, you "have" thirst rather than "being" thirsty. You use the verb ter (to have) for many physical states where English uses the verb "to be", such as ter sede (to be thirsty), ter fome (to be hungry), and ter frio (to be cold).

Why is it muita instead of muito?

Because sede (thirst) is a feminine noun. In English, you say "very thirsty", but in Portuguese you literally say "I have a lot of thirst". The word for "a lot of" must change to match the feminine noun, so muito becomes muita.

Where is the word for "I" (eu) in this sentence?

Portuguese often drops subject pronouns like eu (I) because the verb ending already tells you who is doing the action. The word tenho specifically means "I have", so adding eu is not necessary unless you want to add special emphasis.