How does the serving and swapping side cycle work after the first set?

Question

I know that when you start a match, you spin the racket or toss a coin and decide who serves first and who goes on what side. If you finish a set that's not a multiple of 4, say 6-3, does the person who served last now receives?

Example: Person A serves first on side 1. They keep on playing. Say A wins the set 6-3. A served in the last set on side 1. In the next set, do they swap sides and Person B serves on side 1 or does A serve again on side 1 like the start the first set?

I'm pretty sure it's the first option but when I play some people say you spin the racket again or start again like a new set. When they do it my way, they get confused when to swap sides because the rely on the number of games played, and they don't count the first set.

Answer 1

The first option is correct: Person B serves from side 1.

According to Rule 14 (Change of Ends) in the ITF Rules of Tennis,

The players change ends at the end of a set unless the total number of games in that set is even. As the result of the set is 6-3, the total number of games was 9 (not even), so they switch sides. Since Person B played the last game on side 2, he will start the second set on side 1.

According to Rule 10 (Order of Service),

At the end of each standard game [i.e. not a tie-break game], the receiver shall become the server and the server shall become the receiver for the next game.

So, because Person A served the last game of the previous set, Person B will serve now.

Answer 2

Neither of your options are correct. From the ITF Rules of Tennis (Internet Archive), section 10. CHANGE OF ENDS:

The players shall change ends at the end of the first, third and every subsequent odd game of each set. The players shall also change ends at the end of each set unless the total number of games in that set is even, in which case the players change ends at the end of the first game of the next set.

Also, section 14. ORDER OF SERVICE:

At the end of each standard game, the receiver shall become the server and the server shall become the receiver for the next game.

So in your example, the correct answer is: In the next set Player B will serve the first game from side 2, and they will change ends before the second game of the set.