Learn Portuguese (Portugal): Tenho muito sono.

In English, we say "I am sleepy" using the verb "to be". In Portuguese, you express this as "I have sleep" using the verb ter (to have) followed by the noun sono (sleep). You will see this pattern with other physical feelings too, like tenho fome (I am hungry / I have hunger).

Where is the word for "I" in this sentence?

The word for "I" is eu, but it is completely normal to leave it out in Portuguese. The verb form tenho only ever goes with eu, so the listener already knows who is experiencing the feeling.

Why is it muito and not muita?

Because sono is a masculine singular noun. When muito comes before a noun to mean "a lot of" or "much", it has to match that noun's gender and number. It stays as the masculine singular muito to match sono.

If sono means sleep, how would I say "I am very tired"?

To say you are tired, you switch to the verb estar (to be) because tired is a description, not a thing you have. You would say estou muito cansado if you are male, or estou muito cansada if you are female. Tenho muito sono specifically means you are ready for bed.