Who serves when? Need clarity and understanding.

I need responses in layman's terms, if possible.

I understand that when serving first, the player stands on the right and the score is 0- 0- 2. Are they always the second server or does it depend on the score?

Example, team A doesn't get a point and it goes to the other team, Team B. The other team, Team B, scores 3 points before it goes back to Team A. The score is now 0 - 3 - 1. Who serves? You, the original server at the beginning of the game or your partner who hasn't served yet?