Learn Croatian: Ovdje sam.

Croatian usually drops subject pronouns (like ja, which means 'I') because the verb itself already tells us who the subject is. The verb sam specifically means 'am', so it is clear you are talking about yourself. You only add ja if you want to emphasize who is here.

Can I swap the words and say Sam ovdje instead?

No, you cannot start a sentence with sam. Sam is a 'clitic'—a short, unstressed word. Croatian grammar has a strict rule for clitics: they generally must go in the second position of a sentence or clause. Since it cannot be first, ovdje has to go before it.

If I do want to include the word ja (I), what happens to the word order?

If you add ja, the sentence becomes Ja sam ovdje. Notice how the clitic rule still applies! Ja takes the first position, so the clitic sam must immediately follow it to stay in that required second position.

Is there a difference between ovdje and tu? I have seen both used for 'here'.

Both translate to 'here' in English, but they have a slight difference in distance. Ovdje strictly means 'right here' (very close to the speaker). Tu can mean 'around here' or 'there' (close to the person you are talking to). In casual, everyday speech, people often use them interchangeably.