Be prepared -- going from 20 to 40 will take you a lot longer than going from 1-20. If you're on a PvP server you'll have to level in a contested area (this means you are automatically flagged for PvP), and that means you are likely to be ganked by opposing players who will often be a much higher level than you. If you're on a PvE server there is no threat of ganking unless you flag for PvP or wander into an area held by the opposing faction, but the difficulty level also ramps up here as well. Mobs have more health and do more damage, and you will probably find quests are harder to complete. Generally, you won't need to group up for quests (your bubble and your ability to heal yourself is invaluable), but in many zones it's not a bad idea. Since Blizzard increased the amount of experience gained from quests in this level range, it may be advantageous to group up and finish a quest quickly, rather than do it solo.
As you've probably realized by now, every 10 levels you gain is a milestone: you generally pick up more skills or new skills at these levels, and the next big tier on your talent tree becomes available. Usually I would recommend that you start saving for your first mount at level 20, but paladins, like warlocks, get their first mount for free. Despite that fact, I would still try to save some money, as training your new skills can quickly get expensive. As you level from 20 to 40, make sure to increase your skill in any gathering professions you may have (herbalism/skinning/mining) so that you don't have to spend extra time in lower level areas grinding it up later.
Alright, let's get to the new skills!
Level 22: You get another new aura -- Concentration Aura! You don't need to run with this up all the time, but if you're under attack and need to heal yourself it's best to switch to this first. When combined with Spiritual Focus from the Holy tree, your heals can't be interrupted by damage. Level 22 also gets you new ranks of Holy Light and Seal of the Crusader. Additionally, you get a brand new skill... Seal of Justice. This seal doesn't deal damage but it does have a chance to stun the target. However, its real power lies in Judging it: the Judgement will stop a mob from running in fear when it gets low on health, which is great because running mobs have a nasty habit of pulling other mobs.
Level 24: You get a longer lasting Blessing of Protection and Hammer of Justice, as well as an improved Blessing of Wisdom. You also get a new skill called Turn Undead, which acts as a fear for undead mobs. This is handy since undead are immune to all normal fear effects. If you're leveling an alliance character in Duskwood, you'll probably use this a fair amount there.
Level 26: Your rewards for making it to 26 are new ranks of Seal of Righteousness, Retribution Aura, and Flash of Light, as well as a new skill -- Blessing of Salvation. Blessing of Salvation reduces the amount of a threat generated by 30%, which is excellent to use on DPS-type characters when running instances since it makes it harder for them to pull aggro off the tank.
Level 28: Only two things to train this level: a new rank of Exorcism, and the first of your "Resist" auras. Shadow Resistance Aura does just what it sounds like: increases your shadow resistance (by 30, for this rank).
Level 30: Another milestone! You've probably seen a few new zones now and are ready for more! Before you get back out there, make sure to stop by a city with a Paladin trainer to get your new skills, since there's a lot this level. If you've stayed in the Retribution tree, you can get the talent Sanctity Aura, which increases Holy damage by 10% and should replace Retribution Aura when you're in combat. You also get new ranks of Consecration, Holy Light, Devotion Aura, Lay on Hands and Seal of Command (if you're Ret). In addition, you get 2 completely new skills: Seal of Light, and Divine Intervention. Seal of Light (and its Judgement) have a chance to restore health whenever you hit with your weapon. Divine Intervention is only really useful in instances -- it has a long cooldown, requires a reagent, and kills you when you use it, but it saves your target from death. When used on someone else who can rez in an instance, you've just prevented a wipe (when all your party members die).
Level 32: You get another resistance aura, called Frost Resistance Aura (guess what it does). You also will snag new ranks of Blessing of Might and Seal of the Crusader.
Level 34: Upgrades to Blessing of Wisdom, Seal of Righteousness and Flash of Light are yours at level 34. You also get a new bubble: Divine Shield. This is an upgrade to Divine Protection -- you're still protected from all spells and physical attacks, but the main difference is that you are able to attack while using Divine Shield! The downside to this is that it doubles the amount of time between your attacks, but at least you can do more than stand there and heal yourself now.
Level 36: At level 36 you gain new ranks of Exorcism, Redemption and Retribution Aura in addition to your final resistance aura. This one is called Fire Resistance Aura, and it works the same way your other resist auras do, except for Fire instead of Frost or Shadow.
Level 38: You're probably sick of running everywhere on foot at this point, but you're almost there. Level 38 gets you new ranks of Blessing of Protection, Holy Light and Turn Undead. You also get a new seal: this one is called Seal of Wisdom and it works similarly to Seal of Light, except this grants mana instead of health.
Level 40: You made it! Level 40 is a major milestone because you get your first mount -- nothing compares to the feeling of riding around on your mount for the very first time, especially if it's your first character. I spent hours just riding around when I got my first one. Unlike other classes, who have to shell out a good amount of gold to get the training and purchase their mount, you get yours for free. The other big deal at this level is that you learn to equip Plate armor! You may not replace the Mail you've been wearing for the last 40 levels right away, but you should upgrade as soon as you can. You also get new ranks of Consecration, Devotion Aura, Hammer of Justice, Seal of Command, and Shadow Resistance Aura. If you're staying Retribution, you can pick up Repentance, which acts as a ranged sleep that is usable on human enemies. If you've been eyeballing the other trees, this is a good time to respec. If you want to go Protection, you can pick up Holy Shield and start some serious prot grinding. If the Holy tree appeals to you, you can pick up Holy Shock and start on a Shockadin spec.
With a mount, the world shrinks: you get from place to place much faster than before, which helps increase the speed at which you level, and you have most of the skills you'll use for the rest of the game. But now that you're 40, there's no time to stop: 41-60 can be both the most challenging and rewarding part of the leveling process, and Outlands looms behind 60. There's still a long way to go, but don't get discouraged -- you'll make it if you just keep swinging!