Paladin spells come in several types: Blessings, Judgements, Hands, Seals, and regular cast spells and attacks. Auras are long term effects that the paladin puts into play that stay in effect until cancelled. Blessings are long term buffs (benefits) for the paladin or other characters. A paladin can only have one blessing on each character at a time. Seals serve two purposes, the first is to provide some effect while active and the second is to allow you to use judgment against a target. Hands allow Paladins to protect or heal themselves or other players. The rest of the paladins spells are normal spells just like any other character.
Spells are also sorted by the spec they below too or are general spells. Paladins have abilities that are classified as Holy, Retribution, or Protection depending on the spec that they are key to. Paladin spell and abilitiy damage is either of two basic types: Holy and Physical. While Holy spells generally provide healing ability there are many spells and abilities from all three specs that deal Holy damage. Protection abilities generally provide damage and threat, while Retribution abilities are pretty much all about damage.
Talents and Specializations for any class are important but for a Paladin as a Hybrid class they are even more critical. As a Hybrid class what specialization you choose has a dramatic affect on your character, unlike a single purpose class like a rogue who no mater which spec they choose they still are just there for damage. This is just is not the case for a Paladin. If you choose the Protection spec then you are going to be a Tank, pick the Holy spec and you will be a healer, and lastly if you pick the Retribution spec then you will be a damage dealer.
This is explained in detail when you pick your specialization in the game. Once you pick your specialization you then need to start picking your talents.
Unlike in the past where each Spec got its own talent tree, all specs from a class share the same talent tree. For more information check out the guide here: WoW Talent System 2.0 ( Patch 5.0.4 ).
In short you now gain a talent every 15 levels, can only chose 1 from each tier, and all specs have the same talents. It is drastically different than before so make sure you read the talent system guide above.
A complete talent calculator can be found on the official World of Warcraft site here. It is a great place to start exploring the Paladin class as once you understand the talents that you can gain you are a lot closer to understanding the class itself.
Talent builds change dynamically based what it is that you are looking to accomplish. If you are focusing on healing, DPS, or tanking then you could have very different talents chosen. Talents also vary drastically depending on what you do in the game, a PVE raiders build will look different than a PVP arena player. Lastly, personal choice factors in a lot more than it did before, since each tier has rough themes, such as movemeny, where all three talents grant the same type of benifit but in different ways.
If you want to find some builds or discuss some builds the best place to do so is in the forums, as they are far more fluid and changing than a guide.
You can also check out the official Talent Calculator here: WoW Talent Calculator.