Keep your seat. Fans are expected to stay seated, although movement can take place when play has finished such as changing sides. Again, when you want to re-enter the stands, you will only be permitted to go when play is not underway. You must move quickly as the time may be less than a few minutes and when you return, settle yourself quickly.
Cheer if you like. Many people cheer their favorite on and even applaud wildly for a nice rally and believe it or not, it is more than ok. The players may be somewhat encouraged by this. Unlike other sports you will not find the wave being done, songs sung or chants and foot stomping, but good fan etiquette says bring on the cheering.
Silence the phones! There are moments of intense concentration for the players and the entire stadium will quiet down. A ringing phone can be a terrible distraction, let alone talking on one.
Be mindful of those behind you. Although the weather may be unpredictable, leave the large hats and umbrellas at home. It is hard to see around a large object obscuring the entire court, so if needed make sure they are small and you keep them very low.
Keep comments about players and official calls to yourself. Although you may disagree with a call or a player may rub you the wrong way, comments to either of them are strictly prohibited. At times you may hear whistling from fans in the crowds when a call is deemed incorrect, but good tennis etiquette allows nothing more.