As HotS (Heroes of the Storm, not to be confused with Heart of the Swarm) is getting more popular, I thought I'd write down what I have learned the hard way to help players getting into HotS find success more quickly. This is intended for people who have played a couple of games of HotS already as I'm not going to explain most of the terms. The game is deeper than it looks, and coming from Dota 2 I've had an advantage, but it took me about 10 games before I really started winning regularly. In this article I will cover the basic strategy that should work for public games without getting into map specifics, but the maps really do affect what you will want to do.
Goals of the game
There are only two resources in the game: experience and map control. This is simplified from the classic Dota model of having gold as well, but understand that in this game, everything you do needs to work toward one of these two goals if you want to win the game.
At the beginning of the game, map control is very hard to obtain, so experience is your priority. You need to have at least 1 person in each lane to get experience from the minions that are dying so you don't fall behind. You only need to be near the creeps, so if you're alone in lane, play conservatively and try not to get harassed. You should, in general, try to get objectives, such as the Tribute, even if they cost you a bit of experience, because that will lead to map control, which is the more important of the two objectives. However, getting as much experience as you can to get to level 10 before your opponent is generally the early goal of the game. Experience takes more and more of a backseat in terms of importance as it gets later in the game. You will notice that it's really, really hard to be up by more than a level over your opponent later in the game since it requires so much experience to reach the next level. So what this means is that once you hit level 10, your team should group up pretty much all the time.
This is not an excuse to not help your team in the early game. In public games, sometimes your teammates will group up and fight all the time. If you don't help them, they will give up a bunch of kills and experience so all the experience you worked to gain by staying in lane won't matter, and your teammates will hate you. So if your team is being stubborn, it's okay to group up with them earlier, though this is less than optimal since early kills usually put you behind in experience if you don't have people in the lanes.
So the lesson with experience is to not worry about kills early. They don't give much experience compared to the minions, and whoever you kill will come back with full health and mana in a couple of seconds while you won't have full health and mana.
Map control is the most important thing about the game. This involves doing damage and taking the opponent's buildings, especially their Forts and Keeps. Not only do killing these buildings give your team a boost in experience, it makes it so that lane is always pushing into them and they constantly have to deal with it. This means you are free to take all the mercenaries and objectives on the map. Then eventually you can either just go directly to kill the core along with a mercenary, or try to win a team fight and kill the core while they are respawning. So unlike Dota, where keeping the lane back in the early game is important, in HotS you should always be trying to push the lane and dealing damage to their buildings as much as possible. Use your AOE abilities to keep the creep waves away from your towers and pushing into theirs.
A common pitfall I see with my teammates is that they are very focused on taking all the mercenary camps on the map without pushing along with them. Remember, the point of taking mercenaries is to get map control, and if you just leave them to push alone they will usually just be killed without giving you any (later in the game). That means you just wasted your time to do nothing. So unless you're pushing some other lane so that they don't have time to deal with the mercenaries, or you're pushing with the mercenaries yourself, it is not great to be taking mercenaries. There are a lot of games where my team could have won by just pushing with alongside a Grave Golem, but some teammates want to go take other camps instead. This is a no no and you should encourage your teammates to push with the mercenaries.
You can of course use the mercenaries as a distraction so that the enemy has to choose between losing their buildings or losing a map objective. This is great if you time it well and a perfect illustration of taking a mercenary in order to obtain map control.
Another more subtle way of evaluating map control is how much mana and health you have. Use your Moonwells liberally to keep yourself topped up, especially when a map objective is about to appear. Don't be afraid of using your hearthstone to go back to base to fill up. In this game, "winning the lane" is essentially the difference between your health and mana vs. your opponent's at the time of an objective spawning. So try to bully them off the regeneration orbs, getting to use even one extra ability in the fight can turn the fight!
What to do in a team fight
For MOBA veterans, this section will not be news. For newer players of the genre, read on!
Engagements will happen and are inevitable, so what are some general guidelines you should follow? First, you are squishier than you think. If you need to be chasing someone while a teamfight is still going on around you, it is probably not worth it unless the hero is super high value such as a Nova or Hammer, and even then you need to make sure you get the kill because you are probably going to die. So the best way to approach a fight is to dance around. Use some abilities, and then if people are focusing damage on you, run away, wait for your abilities to come back up, and use them again. Remember that your teammates are all dealing damage while they're chasing you around, and they will likely overchase. Another way to look at it is that you are forcing the enemy to make more decisions in the heat of the moment: If you just run straight at them, their decision is easy, they will just simply kill you. If they start attacking you and you run immediately, they now have to decide if they want to pour more resources into chasing you, if they can even kill you if they do, who to target next if they are going to switch targets, etc.
Second, your positioning is everything, especially with assassin heroes. Never go in before your warriors/tanks, and sometimes just wait out an ability or two from the enemy before jumping in and unloading your fury. I see a lot of Zeratuls racking up the deaths because they go in too early or don't blink out right away. Don't stand beside other heroes so that AOE abilities will catch more than one of you. And always have an escape plan if you go in. With heroes like Valla, that means saving a Vault.
And that's all folks!
Just with these few pointers, you should be well on your way to winning a decent number of HotS games. There are more advanced strategies of course, and map specific exceptions, but you will have plenty of time to learn those. Pick a hero, learn the intricacies of their skills and talents, and pay attention to what kills you. And most importantly, support your team and have fun! HotS is a heavy team fighting game, so if you're alone, you're most likely doing it wrong.