Try to play your normal game.
Be friendly but fair.
Know that league play isnt really that big a deal. Sure, you want to win, your team wants to win, but it's JUST a tennis match.
You've played tennis matches before. This isn't that big a deal.
As for etiquette things....
-Be on time. If your captain wants you there 20 minutes early, try to be there 20 minutes early.
The worst is players who show up for a 7pm match rushing in at 6:58pm still in street clothes.
Don't be that person.
-Be ready to go onto your court, sometimes a few minutes early, sometimes very, very late.
If you are on time, pay attention to the court flow. If it looks like a court might open up soon (check the court score cards, which should generally be updated), and you are the next court to go out, do your bathroom, or your stretches, or your knee brace, fill your water, etc. Be ready to head out when your court is open.
Also be aware that it is unfortunately not unusual for the late matches, matches that start at 9pm etc., are running late from previous matches having also run long. 1/2 hour or an hour after your scheduled start happens. Be aware of this if you are an early match. Your dawdling or chit chat can push back later matches.
-Try to be a decent warm up person. The brief warm-up time is not the time to display your powerful fh, or you work on your drop shot. It is a brief time for both players to loosen up a little. For many, it is not enough time to warm up, so don't waste it. Of course it takes two. Many people play mind games in warm up. They suck as humans imo.
-During play, be fair but firm. Make your calls promptly and fairly. If you are not sure, then give them the point. Pretty simple.
-Know how the tie break works, for the set, and the match.
If you aren't sure, ask your captain BEFORE THE DAY OF THE MATCH to 'splain it to you. Do not hit up your captain to explain it as you are heading out to your court. Trust me. The captain's job is to worry about a lot of items you might not be aware of so you don't have to. Don't bother the captain with questions you could've asked the day or week before.
-Save the socializing for after the match and off the court. Ask about their job, kids, pets, racquet choice, shoe choice, etc. after the match. And if your opponent is chatting you up on change of side, be polite but brief, and simply say "Should we head back out?" is a safe way to indicate that now is not the time to be social. Again, there may be matches to come after yours. Be respectful of this fact.
That said, if possible, when you head out to the court, and if the option is there, set your bag and water on opposite side of court from opponent. This helps limit chit chat on change overs. If you are side by side it is too easy to be friendly and naturally start talking. 2-3 minutes chit chat every changeover adds up.
-If there is a dispute on your court, try to reason it out between the 2 (4?) of you. If after a brief discussion and you both really don't know what to do, ask whichever captain is closest to your court. You can generally trust the captains to tell you an honest answer.
-That said, you should know most of the rules. Things you can do in social play may not be ok in league.
Big one is catching or stopping balls that are flying out of your court. In social we all catch the ball so we don't have to chase it, or to prevent it from goung into another court of play. Not so in league. You must let the ball bounce. Failure to do this IS the opponents point. Even if you are standing behind the baseline and the ball is buzzing at you head high...let it go. If you catch it or stop it, it IS the opponents point. Period. No argument.
-Call the score during your serve and update the scorecard on change overs. This will save A LOT of disputes!
-Be careful with things like over the net or talking when ball is heading towards opponent. Again, little things ok in social are NOT ok in league. Know the rules so you don't break them, and so you aren't being ignorantly taken advantage of.
My experience is most people in league are normal, nice people. 90%+ imo. There are jerks, and cheats, and passive aggressives, and hot heads....hopefully you aren't one of them, but know you will eventually run into them. Comes with the territory.
Play hard, play fair, be on time, don't waste time, know the rules. Good luck!