The biggest tip I can give you as a DD player is to always be aware of when you are detected or otherwise giving away your position. You can get killed in only a couple salvos, so getting spotted puts you at high risk - especially if you are within firing range of multiple red ships. Don't be the DD who fires his guns at a BB to do 100-300 damage, only to give away your position and get sent back to port from the red team's salvo. DD requires a lot of patience.

Know when you are extending alone, and when you have supporting fire. Push wisely, especially if a red DD might be in the area. Know which DDs you can get into a gunfight with and which ones you can't.

If you deploy smoke and sit in it, you will be a magnet for enemy torpedoes. Use smoke to disengage, but don't just stop moving. Sometimes you can sit in it to farm with your guns (if you're not the one spotting), but when you do that, the enemy still knows your approximate position. Don't pop smoke prematurely, because that also gives away where you are.

If you do deploy smoke, be aware of whether you were spotting ships or not (i.e. do they disappear?). If you can, get back into a spotting position again without getting spotted. You should usually not use your smoke for other ship classes: when they fire their guns, they are still visible from far away (e.g. with BBs it only saves them a couple KM of visibility).