Among any sets in the game there is only a basic set of cards (both simple and gold versions), which can be fully obtained only via levelling up your heroes. The level of a hero grows with every played game and the more cards you played during the match, the faster it happens. Each time after a match when the game reports about level progress, you can hover over the strip of experience and know at what level you will find the nearest reward card, and which card it will be.

A gold version of cards also can be played by using the gold card with summoning ability - for example, gold Unstable Portal will give you gold cards into the hand, but only increasing the level of the hero will give you these cards in your personal collection.

Tables below shows you at what level and which cards the game gives as a reward for diligent progression of a hero.

Class cards

Class cards can be put in a deck only for "their" hero. Abilities of some cards - for example, Nefarian - can get class cards in a hand for a hero of another class.

Cards derived for a hero from the start

Simple cards from the list available in your collection once you start playing this or that hero. All of them are issued by pairs. Gold cards are issued successively, one by one; levels at which they can be obtained are given in the last column.
 
 
 
Timber Wolf
Tracking
Arcane Shot
Multi-Shot
Houndmaster
 gold
23, 26
15, 20
32, 34
36, 38
28, 30
 
 
Wild Growth
Mark of the Wild
Claw
Innervate
Healing Touch
 gold
23, 26
28, 30
32, 34
36, 38
15, 20
 
 
Arcane Intellect
Fireball
Polymorph
Arcane Missiles
Arcane Explosion
 gold
15, 20
44, 46
47, 48
32, 34
28, 30
 
 
Sinister Strike
Assassinate
Sap
Deadly Poison
Backstab
 gold
15, 20
47, 48
40, 42
43, 44
36, 38
 
 
Light's Justice
Hand of Protection
Hammer of Wrath
Blessing of Might
Holy Light
 gold
36, 38
23, 26
32, 34
45, 46
15, 20
 
 
Northshire Cleric
Holy Smite
Mind Blast
Power Word: Shield
Shadow Word: Pain
 gold
40, 42
23, 26
15, 20
47, 48
36, 38
 
 
Ancestral Healing
Rockbiter Weapon
Frost Shock
Windfury
Hex
 gold
15, 20
36, 38
32, 34
23, 26
47, 48
 
 
Voidwalker
Succubus
Hellfire
Drain Life
Shadow Bolt
 gold
36, 38
40, 42
49, 50
45, 46
47, 48
 
 
Warsong Commander
Fiery War Axe
Execute
Charge
Heroic Strike
 gold
36, 38
49, 50
47, 48
23, 26
15, 20

Cards derived from the increasing the level of a hero

Simple cards from the list are issued by pairs, golden ones are issued successively, one by one. The first column shows the levels at which you'll receive a pair of simple cards, latter column tells the levels that must be reached for the gold versions.
 
 
 lvl
2
4
6
8
10
 card
Animal Companion
Starving Buzzard
Hunter's Mark
Tundra Rhino
Kill Command
 gold
45, 46
47, 48
40, 42
43, 44
49, 50
 
 lvl
2
4
6
8
10
 card
Starfire
Savage Roar
Moonfire
Swipe
Ironbark Protector
 gold
45, 46
43, 44
40, 42
47, 48
49, 50
 
 lvl
2
4
6
8
10
 card
Frostbolt
Mirror Image
Frost Nova
Water Elemental
Flamestrike
 gold
40, 42
36, 38
23, 26
49, 50
51, 52
 
 lvl
2
4
6
8
10
 card
Assassin's Blade
Fan of Knives
Shiv
Vanish
Sprint
 gold
32, 34
28, 30
45, 46
23, 26
49, 50
 
 lvl
2
4
6
8
10
 card
Truesilver Champion
Consecration
Humility
Guardian of Kings
Blessing of Kings
 gold
40, 42
43, 44
28, 30
47, 48
49, 50
 
 lvl
2
4
6
8
10
 card
Divine Spirit
Mind Vision
Holy Nova
Shadow Word: Death
Mind Control
 gold
28, 30
32, 34
45, 46
43, 44
49, 50
 
 lvl
2
4
6
8
10
 card
Bloodlust
Flametongue Totem
Totemic Might
Windspeaker
Fire Elemental
 gold
40, 42
43, 44
28, 30
45, 46
49, 50
 
 lvl
2
4
6
8
10
 card
Corruption
Mortal Coil
Soulfire
Sacrificial Pact
Dread Infernal
 gold
32, 34
43, 44
28, 30
15, 20
23, 26
 
 lvl
2
4
6
8
10
 card
Cleave
Kor'kron Elite
Whirlwind
Shield Block
Arcanite Reaper
 gold
40, 42
44, 46
32, 34
28, 30
51, 52

General gold cards, received from the increasing the level of a hero

Cards from this list may be contained in a deck of any class, simple versions of them are availiable to a player from the scratch, but only increasing the level of heroes may result a gold version as a reward.
 
 
 
Core Hound
Stonetusk Boar
Razorfen Hunter
Bloodfen Raptor
Ironfur Grizzly
 lvl
51, 52
53, 54
55, 56
57, 58
59, 60
 
 
Oasis Snapjaw
Nightblade
River Crocolisk
Elven Archer
Novice Engineer
 lvl
51, 52
53, 54
55, 56
57, 58
59, 60
 
 
Dragonling Mechanic
Ironforge Rifleman
Archmage
Dalaran Mage
 lvl
53, 54
55, 56
57, 58
59, 60
 
 
War Golem
Murloc Tidehunter
Voodoo Doctor
Acidic Swamp Ooze
Sen'jin Shieldmasta
 lvl
51, 52
53, 54
55, 56
57, 58
59, 60
 
 
Stormpike Commando
Bluegill Warrior
Stormwind Knight
Goldshire Footman
Stormwind Champion
 lvl
51, 52
53, 54
55, 56
57, 58
59, 60
 
 
Murloc Raider
Shattered Sun Cleric
Darkscale Healer
Gnomish Inventor
Lord of the Arena
 lvl
51, 52
53, 54
55, 56
57, 58
59, 60
 
 
Magma Rager
Frostwolf Warlord
Booty Bay Bodyguard
Frostwolf Grunt
Reckless Rocketeer
 lvl
51, 52
53, 54
55, 56
57, 58
59, 60
 
 
Boulderfist Ogre
Grimscale Oracle
Ogre Magi
Gurubashi Berserker
Kobold Geomancer
 lvl
51, 52
53, 54
55, 56
57, 58
59, 60
 
 
Silverback Patriarch
Chillwind Yeti
Raid Leader
Wolfrider
 lvl
53, 54
55, 56
57, 58
59, 60
Source of this information can be found here. Have a good game!

Some more words about gold cards

And of course, if you want to collect more gold (and basic) cards, you can
  • craft them from the dust, which can be obtained on the arena, with disenchanting cards or from seasonal award chest. This is the only way to get a gold versions of adventures cards;
  • get them out of the booster purchased for real or in-game money, or received for winning the arena and in the brawl;
  • get them out of the award chest, that issued at the end of the season, and which content depends on the rank that has been made in the season.