Welcome! If you are here then I am assuming that you are new, need help and love Paladins. If that is the case sit tight and be patient, because this topic will be fairly lengthy. However, my hope is that it will be useful.

So, let's get started: the Paladin has two basic play styles that are viable. One is an Aggro-Paladin and the other is a Control Paladin. I will cover both, however I personally prefer the Control build. I'll have to start with the control build because the aggro build is literally impossible to build without certain cards and a wide range of cheap minions.

Control Paladin - basically you want to grind your opponent down. A few goals would be establish board Presence, maintain board presence and keep your opponents field clear. Pretty straight forward. So here is a completely f2p version, which will be followed up by a list of cards to think about crafting to improve deck quality and maintain a control build.

Acidic Swamp Ooze × 2
Holy Light × 2
Novice Engineer × 2
River Crocolisk × 2
Razorfen Hunter × 2
Shattered Sun Cleric × 2
Wolfrider × 2
Chillwind Yeti × 2
Consecration × 2
Hammer of Wrath × 2
Truesilver Champion × 2
Darkscale Healer × 2
Stormpike Commando × 2
Boulderfist Ogre × 2
Guardian of Kings × 2

This deck should give you decent winning chances, but it will be a tough road against players with a larger card pool. Some cards to consider crafting and what to potentially replace with them:

Equality x2 replaces Holy light
Pyromancer x2 replaces Novice Engineer
Aldor Peacekeeper x2 replaces Razorfen Hunter
Harvest Golem x2 replaces Wolf Rider
Earthen Ring Farseer x2 replaces Shattered Sun Cleric
Sunfury Protector x2 replaces River Crocolisk
Ancient Watcher x2 replaces Acidic Swamp Ooze
Defender of Argus x2 replaces Stormpike Commando
Azure Drake x2 replaces Darkscale Healer

Those are all strong cards that can do nothing but improve your deck quality and improve your winning chances. The italicized cards have incredible synergy and are the best board clear in the game. You play Pyromancer and follow with Equality and you clear the board almost no matter what (if something has a divine shield you will have to pop it first). The cards in bold are often called the Watcher Suite. They are called this because the Ancient Watcher is a 4/5 for 2 mana, and if taunted, is a very cheap but strong taunt, and Sunfury and Argus both give taunt to adjacent minions. There are other cards that are great to craft and add, however I didn't include them because they are either epics/legendaries or are more of a preference and wouldn't necessarily improve deck quality. For the Paladin deck I am currently running visit my Climb the ladder thread.

~~~~

Aggro-Paladin - basically, you fill the field with as many 'fast' minions as possible to overwhelm your opponent and quickly drop your opponent to 0 health. This deck build relies on certain essential cards, and some cheap common cards, but it is NOT a completely f2p deck list. This list will also include good options for crafting to replace cards.

Abusive Sergeant × 2
Argent Squire × 2
Blessing of Might × 2
Leper Gnome × 2
Acidic Swamp Ooze × 2
Argent Protector × 2
Dire Wolf Alpha × 2
Loot Hoarder × 2
Divine Favor × 2
Harvest Golem × 2
Scarlet Crusader × 2
Shattered Sun Cleric × 2
Wolfrider × 2
Consecration × 2
Truesilver Champion × 2

That is a basic deck list for aggro. The key card is Divine Favor. Unlike Warlock Paladin doesn't get to draw 2 cards per turn if wanted. So, you spam the field and drop Divine Favor to replenish your hand. It is a fairly cheap deck and definitely not the best, but it has good winning chances and decent deck quality. Some good options to craft would be:

Sword of Justice
Young Priestess
Blood Knight
Arcane Golem
Defender of Argus
Coldlight Oracle

There are other good options, and a lot of them will likely be more of a play style preference. I hope this has been informative and given a basic idea for deck options. Good luck all.