When playing as Support, smoke grenades can help you rescue your teammates, especially in a crowded area. Use them well, and you'll revive your team like a angel.
When locking onto a vehicle as Engineer, don't fire until the enemy deploys countermeasures. (flares, smoke, etc.) The enemy will be left vulnerable and you can fire your rocket with no worries. Sometimes the enemy knows about this tactic, so be careful.
You can also ask a Recon to laser mark enemy vehicles, this will make it so that you can lock on quickly, and it can make it so that you can lock onto aircraft with a Javelin, or a tank with a Stinger.
Speaking of Recon, you can deploy onto a friendly Helicopter and parachute onto a rooftop, then you can deploy your respawn beacon. This will give your team a great vantage point to snipe from.

Make sure you use the right loadout for your weapons and vehicles. Experiment with attachments on the firing range, and see which ones are right for you. You can also calibrate certain attachments for mobility or for accuracy. For vehicles, change your loadout depending on your playstyle. (anti-tank, anti-aircraft, anti-personnel)
You can also use XP tokens to boost a weapon's level. Use them when you don't feel like grinding.

Stick with your team. The battlefield is dangerous and you can die in seconds. You will have to adapt to every map and every enemy type.