What is the fastest way to level a hero to level 10?

I've two heros to level 10, and now I got a daily quest that is specific to two classes that I still have at level 1. Winning with those with a basic deck lacking any of the cards you gain on the way to level 10 looks very unlikely. I've played reasonably successful with my mage, so my opponents now are a bit too strong for a level 1 basic deck.

Levelling with practice games against the regular AI is tediously slow and boring. But playing casual or ranked games seems mostly suicide without it, though it might be an option if the XP gain even when defeated would be higher than in practice. Or should I play against the expert AI?

Which is the fastest way to level up my heros to 10 so that I can properly use them with all the basic cards?

Solution 1:

The fastest way to level is hands down by playing games against real opponents. This can be done in either play mode or Arena.

Arena may be best (if you're doing well for gold or don't mind spending the money) because you get to use cards you wouldn't have and the wins and losses still grant you experience. The arena cards you get to use would grant you a stronger deck for that class and would give you (a theoretically) high chance to win than with the basic decks you have. Please note that you will only have the option between 3 classes in arena and may not get the one you need to level (credit: ChrisHateZ)

You can still create custom decks even at low levels. Whatever common cards you may have earned can help in this cause so you can build stronger decks. In play mode, you can gain the experience in either casual or ranked. There is no experience difference gained there, just your ranking.

Also, games that last longer (in the same level) generally give more experience than quick ending games in my experience.

The only reasons to play against the expert AI is to test a deck you are building before putting it out into real play and to complete the quest that requires you to defeat all Expert AI opponents (which will reward you will gold).

Solution 2:

Fastest way to level up your heroes to level 10 is to do the practice matches with each of them. Until you reach level 10 with a hero, beating the AI gives the same amount of experience as beating a player. However, when playing against AI, you don't need to wait for the spinning wheel to find an opponent. Finally, the training AI is usually easier to beat then the real players, unless the opponent is AFK, then it's a matter of waiting 3 minutes.

Starting at level 10, you get less experience from the practice matches, and you should play against real players.