Learn Portuguese (Portugal): Eu vou à clínica.

The word à is a contraction. It combines the preposition a (to) and the feminine word for 'the', which is also a. In Portuguese, when 'to' and 'the' bump into each other before a feminine noun like clínica, they merge into à to mean 'to the'.

Does vou mean 'I go' or 'I am going'?

It can mean both! European Portuguese often uses the simple present tense to describe what you are doing right now. So vou (from the verb ir, meaning 'to go') naturally translates to 'I am going' in this context.

How would I change this sentence to say 'I have to go to the clinic' using the ter de structure from this lesson?

You would use the 'I' form of ter (to have), add de, and then use the infinitive (unconjugated) form of the verb 'to go', which is ir. The sentence becomes: Eu tenho de ir à clínica.

Can I drop the word Eu and just say Vou à clínica?

Yes, absolutely. Because vou is exclusively the 'I' form of the verb ir, people will automatically know you are talking about yourself. Pronouns like Eu are often left out unless you want to emphasize that you are the one going.