Leveling up your account in Heroes of the Storm is relatively fast until you get to around level 25 at which point you will find the levels start to go by very slowly. Lets look at some ways you can improve your xp gain.
I don’t think co-op is so great
If you want to level up quickly to start playing ranked matches and would prefer to co-op until that point then you will be entering ranked with much less hero knowledge than you would if you used quick matches to level up. To be honest, until Blizzard updates the matchmaking system then some quick match games are just as good as ranked games and have a good level of strategy and lots you can learn from so the only real difference between co-op and quick match is the points system and the picking phase.
Play with a friend
If you play with a friend (Battlenet friend) in your group then you will both get +50% xp gained from the match. This is a huge bonus and it means that by the time you get to level 21-22 (ish) you would actually be level 30 if you had been grouped all this time.
What is better than 1 friend? Lots…
Group up with your friends, pick your best heroes and crush all the games you enter. This will net you lots of fast wins and a lot of experience. If you are the type of person who does not mind relatively boring games (lets face it, always winning can be boring if the games are never close.) then this is a nice way to level up quickly and practice with your friends to prepare for 5v5 ranked play at level 40.
Purchase a stimpack
If you have some money spare, consider buying a stimpack that will not only double your xp gained but also your gold earned. The gold gain is important as you will be unable to enter ranked mode unless you own 10 or more heroes and if your experience is increasing very quickly then you will find that at level 30 you cannot purchase 10 heroes.
Note: You will get a free 7-day stimpack upon reaching level 10.
Win more (duh)
Experience you earn during a match is also converted to experience your profile gains. The amount gained depends upon your team level and the enemies level so it is not possible to put a definite amount on each objective/on a kill. Needless to say, you earn a lot more xp if you destroy objectives and win the game instead of losing slowly.
Remember to enjoy the game
Sometimes people are so caught up in trying to level fast that they lose track of what is important. Enjoy the game you play and the levels will sail past! You will also find yourself learning more about the game which will translate into you being more skilled at the game.