After about ten and a half months of being chazan 3 times a day - some of what I have learned.
1. Answer the chazan's kaddish and brachos. It has happened many times [tonight it happened again] that I have said יתגדל ויתקדש שמיה רבא and ... silence. Or during chazaras hashatz - almost complete silence after brachos. [The unspoken reality is that people are bored and are daydreaming but that is not a good excuse]. Besides not conforming to halacha - it is also a bummer for the chazan.
2. Sing along when he is singing. Many chazanim aren't comfortable doing solos and it is a great feeling to have the tzibbur "getting into it". It is also good for the tzibbur's davening.
3. Say thank you after davening. "Shkoyach" is nice but thank you might be better. You can say BOTH! The chazan did you a huge favor. He enabled you to fulfill your obligation and more importantly - connect to Hashem! And he worked hard. Being a good chazan requires effort. HAKARAS HATOVVVVVV!!!!!!!!!!!!!!!!!!!!
4. Don't tell the chazan when to start chazaras hashatz [or kaddish after shmoneh esrei at maariv]. You JUST SAID ונפשי כעפר לכל תהיה. You are the dust of the earth to EVERYTHING!! How can one decide five seconds later that he is the chazan's boss [because he wants to get out of shul earlier and feels - we might suggest - a bit imprisoned there]? If the chazan needs to someone to tell him what to do - he can go home to his wife!! That is enough. He might also have a boss at work or parents who tell him what to do. He doesn't go to shul for that. It is demeaning to many or at least a lack of respect. He can count and knows when to start....
5. If you have criticism - think a hundred times before expressing it. Remember - people have negativity bias. If a chazan led the entire tefilla BEAUTIFULLY but skipped one word - let us say that he said המברך את ישראל בשלום and skipped the עמו, we would only notice the missed word and not all the words he DID say. Or if he said המברך את עמו ישראל בשצום - we would only remember that and forget everything he pronounced correctly. People only notice the referee when he makes [what they think is] a BAD call. If you have to say something - first tell him all of the things you like about his tefilla, his taste in clothing, his good looks etc. and then add "by the way, it is kedai to say kedusha louder so that the people in the middle of shmone esrei hear you and can have kavana to be yotzei שומע כעונה". Then hug him and tell him about a shidduch you thought of for his 31 year old daughter.