Well, I wouldn't call myself good, but I do play the app quite a bit. (Which, seconded, app is very good. I believe these days the app + base set is free, and you're paying in-app for expansions only. Try to play online more than against the AI -- the AI is competent, but it's programmed to maximize the points it gets each turn, instead of thinking more long-term. Humans won't make this mistake.)
Always keep an eye on the honour pool. The game changes at about the point there's a third of the initial points left. Early game, play to set up your deck to do powerful things. Late game, that's irrelevant -- you need to make the plays that get you the most points right away. So a card like Arbiter of the Precipice is extremely powerful early (as above), but absolute crap late game. Paying 4 runes for 1 point is a miserable rate of return, and if you buy it late you're unlikely to even see the card in your hand before the game ends. On the other hand, Arha Templar doesn't do enough to be worth buying early, but 4 runes for 3 points is a great rate late game.
Every time you buy a card, another card comes out. This means if you're using up all your runes to buy something in the centre row, your opponent gets first crack at whatever replaces it. So if the centre row is weak, it may be better to take nothing from it rather than potentially giving your opponent a better card. Also, if you're planning to buy two cards on your turn from the centre row, a decent rule of thumb is to buy the cheaper card first. That way, you're the one who gets first shot at a new card. (This is also why Seer of the Forked Path is good. Essentially, Ascension is like an MTG booster draft. Seer is the only card that lets you hate draft without expending any of your resources.)
There's essentially two major strategies. The power strategy is kind of like an aggro deck in MTG -- buy the cards with power, focus on killing monsters and draining the honour pool as fast as possible. Since Void is the power faction, this usually also lets you get your deck very lean, since Void is also good at banishing cards. This strategy needs commitment -- you need to end the game before the stronger cards your opponents are focusing on matter. On the other hand, there's a rune-based strategy where you buy up cards that let you buy bigger and better stuff. This doesn't require the same commitment, but does require timing -- at some point you need to turn that engine into getting power to kill monsters (or Lifebound cards to gain points directly) so you can end the game. You need to figure out when to make that switch, based on what your deck looks like and how much time you think is left in the game.
As for factions:
Enlightened is best at drawing cards. Void is best at banishing cards. Either of these are oil for your deck's engine. You want to see the cards you buy as much as possible, and these get you there. Also, they're the most flexible colours -- you can just get a card and know it'll be good in anything.
Lifebound is best at runes, and can also get you points directly from the honour pool. These will clunk up your deck a bit (there's a bit of card draw but not a lot). Lifebound (the direct points part) and Void are the aggro colours.
Mechana has the most constructs, and the constructs here are always the same number of points as you paid. On the other hand, individually the constructs don't do much. This faction is by far the most parasitic. If someone's allowed to buy up all the constructs and make them into a synergistic machine, they'll usually run away with the game. But if they can't, either because the constructs don't come out or there's multiple Mechana players at the table, this strategy tends not to work out. (Though absolutely buy these on sight late game if possible. There's no better return on investment in the game.)
ascensiongame.com/board has a strategy section you may want to check out.
Finally, you're allowed to do nothing on your turn. This doesn't come up much, but there are spots when it's useful. (For example, you're the last player, you're behind and have a weak hand that could still end the game. It's probably better to just pass, in the hopes of getting one more turn with a stronger hand.)