How do I give a decision, and how do I talk to the main umpire?

A batter is only given out if the fielding side appeals ("Howzat?"). For a run out at your end, if the batter is out, raise your index finger. If they're not out, you don't need to signal; just say "not out" if asked.

Before the game, agree with the main umpire how you'll check with each other on close calls, for example a hand on the chest for "not out". If they ask you about something you didn't see clearly, say so.