a) Single-lane focused pushing: This kind of pushing is most effective in the middle lane. You can quickly gain an upperhand if you take down the first two towers before 20 minutes. Exploit and capitalize on the enemy's mistakes and use it to your advantage. When your opponent laner decides to go to the river for a rune, you should quickly use that time to get down the towers instead of going after him (no point anyway, because he went before you and you can't beat him to the Runes unless you're on a steroid movement speed skill). But sometimes, a problem arises. When you push too far in one lane, enemy heroes tend to group together to protect it. When this happens, you should quickly shift focus to another lane and try to get down a tower with YOUR ALLIES (in unorganized games, enemy players will expect individual heroes on your team to go to different lanes and farm on your own, so they won't come after you when you're shifting lanes). You can establish this type of lane-pushing by being strong early game and forcing them to play passive. Common when there are two ranged heroes vs. melee heroes. When an opportunity presents itself, exploit it by pushing further. Don't miss out an opportunity to push. Ever.
b) All-lane slow and steady way: Pushing this way is more common when you're matched up against opponents of similar skill levels. There are no drastic and revolutionary pushes here, and the game usually takes on a very monotonous and predictable path. When this happens, games are usually won purely by outfarming or outganking and by establishing hero dominance.
2) Hero killing and Ganking: Second best way to win a game. Ganking not only makes you stronger, but also makes your enemy weaker. By constantly and continuously ganking, you can really set back your opponents. They start to play passive, and grow a sense of fear. Doing so establishes psychological dominance and they tend to give up focusing on farming, counter-ganking and stuff, and instead just SURVIVING. Note that you have to balance farming and ganking. Hero kills are better than just farming because of the massive EXP they give. But that doesn't mean you shouldn't farm at all. So here's the next one --
3) Outfarming your opponents: A sure-shot way to win, and just a LITTLE less important than the above. Items often determine a game. They're what allow a carry hero to carry. Watching an overfarmed Troll killing you like ants isn't an uncommon or surprising sight. Ganking and killing is all well and good, but if you don't atleast TRY to farm, you're going to lose out on items (unless you're getting all the hero kills). Farming this way is good, because you have a back-up in case your enemy Troll just escaped a few ganks with 5 hp and is now saving up gold.
All this said and done, this hierarchy is in fact situational. It often depends on the in-game situation, so what you do changes accordingly. But this should give you a general idea of what's important and what's not. There are loads of other factors which are purely specific, but I couldn't possibly shoehorn all of it into this post.