MRD, NIN, and DRG are the classes I'm most experienced with, so this will be catered to that type of play style. I'll direct all these tips for Dragoon, but hopefully something can be taken out of this for all classes. Other experienced players may do things differently, so take all this as preference. Everything here may not necessarily be the best way, just an idea of where to start.
If you're serious about winning and playing effectively, then you should definitely find others on your server and party up. I have an amazing group and an LS filled with skilled players I party with, so I would encourage everyone to do the same. Finding other players to improve with, and as you become more skilled, know you can rely on, makes the experience much better. I know it's frustrating starting out, there's a lot to get adjusted to compared to the PvE content, but don't let it discourage you. Check to see who else is playing from your server and see if they're interested in running matches sometime.
Equipment: Gearing up effectively
For Dragoon it's simple. Level 80+ gear with secondary stats in CRIT and DET. You can also pull off wearing i70 PvP gear w/morale bonus which bumps it up to i80. If you're unsure which gear is better just test it out in a match and see which gives more. If I had to choose between CRIT or DET, it would be CRIT.
Judgement: Knowing who to target
This is very important, and can be a factor in determining whether your team wins or loses. To keep it simple, going into a battle fresh (with all cd's up) your goal should be to kill a healer ASAP. Notice your enemy's party setup, and who on your team is targeting who. If the opposing party has 3 healers, and everyone in your party has been attacking the same one for the past 2 minutes with no sign of killing it, that ain't right. Keep pressure on all the healers then maybe eventually you can take them out. If you notice a BLM casting freely, then you might want to target it instead. Know what your party is capable of. Go for the kills. If you've been pressuring the same healer for a while, and you notice a Ninja at 30% health, it might be worth it to switch targets and take him out. For me it's: Healer > Ranged > Melee > Tank. However, an opponents health trumps all of that if I can get away with a kill. Dragoons have great gap closers so use them to your advantage.
Dragoon actions
Make full use of sprint! Pop Enliven, Invigorate or an Icarus Wing afterwards to replenish your TP. Keeping up with your target is a must if you want to get off a full rotation.
If you can afford to, use Feint on spellcasters! The 20s slow makes a huge difference on them. When I started out on DRG I didn't even know it affected their spellcasting, I thought it was just a small reduction to movement speed.
Be cautious of your stuns! It may be worth the extra damage, or may not be if the target becomes immune.
Weave Keen Flurry, Featherfoot, and Bloodbath in between your actions during fights. The recasts aren't that long and it will help during engagements.
Striking Dummies: Practicing your rotation
In between ques head to the Wolve's Den and strike those dummies. Come up with an effective rotation to use when you go into a fight, fresh. Keep in mind when in your rotation the stuns hit, and try do the most damage ASAP. Perfect your burst. Practice on the dummies while moving and switching targets. You gotta switch to a low HP target fast in order to get that kill, before the healer gets to them first.
Know when to push, hide, or retreat
Sometimes I get this wrong and make bad choices. I feel for my healers when I push too far into enemy territory. But a lot of times I make it out alright because I have great heals. Keep in mind if they are around or not. If they all die on the flag, your team might want to retreat rather than feeding the enemy points for the rest of the kills. If you capture a point solo and choose to stay around, you should probably hide behind a wall or something in case a party comes. That way you can call for backup, or wait until they leave to recapture.
EDIT: I'll go over some rotations in depth later and add more to this. If you want to check out a full frontline match as Dragoon here it is. https://www.youtube.com/watch?v=yIHib6tpGYQ