Strengths & Weaknesses
Paladins are the premier PvP healing class, because they have high damage mitigation, fast, heals, and the ability to all but prevent interrupts from damage. They also have some excellent buffs to give any players they are grouped with or healing. Most importantly, they have the ability to become invulnerable for 12 seconds, which is invaluable in any situation.
The main weakness the paladin has is a lack of any ranged attack. This means that you have to be up close and personal with your opponent to deal any damage. This, coupled with the lack of speed boosting or opponent slowing moves can be difficult. The talent Holy Shock can make up for this, as can the different engineering bombs.
However, this should not trouble a smart paladin. The idea of effective PvP with a paladin is not to deal huge amounts of damage, it is to support your allies as best you can. Team up with a warrior, rogue, or mage, and see where the true power of the paladin. Let them do the brunt of the damage while you keep them healed. Help out with well timed stuns, and finish off with Hammer of Wrath.
Watch your buffs for opponents purging. They will remove your seals and blessings. Seals are extremely important to keep up at all times; blessings less so. Additionally, you should know when to cleanse. Debuffs can cause significant amounts of damage, and cleanse is a cheap way to prevent that. However, some players can force you to waste mana by casting low ranked spells, and as mana is so important, this can be an effective tactic.

As with every class, TRAIN FIRST AID! Often paladins/other healers don’t bother to do this, because it seems unnecessary due to their innate ability to heal. However, mana is difficult to recover, while bandaging is quick and effective. This is particularly true for paladins, who can use Divine Shield in the middle of a fight, and bandage to full without interruption. Use your mana first, but don’t run around doing nothing while your invulnerability is up.
Lay on Hands is a latch ditch heal to save your ass at the cost of all your remaining mana. It should only be used once all other options have been exhausted, but don’t forget about it! It has a long cooldown, but if you can use it to squeeze out a final cap in WSG or kill an annoying opponent it is worth it.
Paladins are particularly reliant on mana, so if you run out, you are in trouble. If you are facing a paladin, use abilities that will drain their mana/make them use it, like snares (to force them to use Blessing of Freedom) or Mana Burn.
General Strategies
Blessing of Freedom is one of the best spells for PvP, specifically for WSG. This removes roots and snares, and gives alliance flag runners a significant advantage. Use it on druids and preparation rogues. Don’t try and carry the flag yourself unless there is no better class around. You are much more effective sitting back and healing/buffing/cleansing the flag carrier.
Get a good cleanse mod! Decursive is excellent, although it will be disabled very soon. However, there will be replacements that help with PvP cleansing. In the meantime, bind cleanse to a key and do it manually. It isn’t that hard, and really, really helps your team out.

Paladins make good defence, due to their stuns, but they really shine at offensive support. Find a partner and follow them around. Make sure you are communicating (through vent, whispers, or battleground chat). If you are on your own, fight back, but let people know where you are and try to stay alive for backup to arrive.

Paladins are much more powerful than people realise. Despite the fact that they can’t put out significant DpS, they can really change the tide of battle. It takes skill and finesse to play an effective paladin, but if you do so you can really help your team out.
Macros
Autobless
This will automatically select a blessing to be cast on a player depending on whether they use mana or not.
/script power = UnitPowerType("target"); if ( power == 0 ) then CastSpellByName("Blessing of Wisdom") else CastSpellByName("Blessing of Might") end; if ( SpellIsTargeting() ) then CastSpellByName("Blessing of Might"); TargetUnit("player"); end;
Arenas
Unfortunately for all you Retribution and Protection paladins out there, healing paladins are essentially the only version of the class played in arenas. That having been said, they have the potential to be the best and most important class.
Healing, spell crit, and most importantly stamina are stats that a healing paladin should be aiming for. Resilience is also very nice to have, and comes on a lot of arena reward gear. Blessing of Sacrifice needs to be used every fight on someone who is going to take some damage, otherwise you are vulnerable to CC. Most teams will try to force a shield early by using CC on you. If you have to use it to save someone – do it, but otherwise try and save it for when you are getting beat on.
While paladins are excellent healers, they lack any kind of group heal, and thus rely on a backup healer in group situations. Shaman are excellent as they excel at healing groups but are weaker single-target healers.