Perhaps the most fundamental question you should ask yourself at the start of a game of Dominion is "how will this game end?" Correctly determining whether the game will end through the depletion of Colonies, Provinces, or via a three-pile ending is critical to creating a strategy that can be the winner at that end of the game. Cards which may be excellent in a Province game could be terrible in a three-pile game or a Colony game.
This article will explore the various ending conditions, how to determine whether your game is likely to end in that condition, and what that will mean for your tactics.
Colony
When Colonies are available, depletion of the Colony pile is typically the way the game will end. Unless you see strong reason to believe that there will be a three pile ending or (very unlikely) a Province ending, you should plan on a Colony ending in a game where Colonies are present in the first place.
Colony games are very likely to be the longest types of Dominion games. They give you more time to build a stronger deck, and are the easiest kind of game to win with an "engine" deck. Obviously, they also require a stronger deck in order to consistently hit the $11 target buy. If a game is likely to end with a Colony depletion, then you can look at the higher tier of Action cards ($5+) and reasonably build your deck around getting a bunch of those cards, rather than just a few crux cards, even without cards that rapidly improve the buying power of your deck.
When you expect a Colony ending, it takes a higher class of card to be useful in your deck. Your end-game expected hand value needs to be $11+. That means that cards that are worth only $2 in your hand (like Silver) are not themselves pulling their weight in a Colony game. Of course you can use Silver (and Copper), particularly with strong card drawing, but you don't want to weigh your deck down with a bunch of copies of cards that only are worth $2 in your hand. It can be tempting to get lots of Silver or similar cards (terminal +$2 actions, for example) in your deck early, as a way to afford the higher-cost Actions, Gold, or Platinum, but remember that you won't love those cards in the late game.
Province
Most Dominion games end with Province depletion -- specifically, most Dominion games without Colonies available end through Province depletion. When Colonies are on the board, it is very rare for Province depletion to end the game, and should almost never be planned for. But when Colonies aren't available, the default is to assume that the game will end with Province depletion, unless you see a strong reason to believe there will be a three pile depletion.
Province games are what you should have the most experience with. They reward rapid engines and modified big-money strategies. Copper is overall a negative in the late game in Province decks, but Silver is fine, delivering well more than the $1.6 average value needed in a card to produce the $8 hands that you're aiming for. Many engine decks are just too slow for Province games, producing a deck that's very strong in the late game, but which is already suffering from a 2 or 3 Province deficit to a faster, Big Money-esque game. If you build an engine in a Province game, you should do so knowing that either:
1. This is a particularly fast engine.
2. This is a particularly strong engine, able to guarantee you multi-Province buys to come back from your deficit.
3. The game is likely to be slower than usual, probably due to Attack cards.
Three Pile Depletion (End Game)
A not-very-interesting type of Dominion game endings is the late game three-pile depletion. This usually happens when there are a small number of Provinces or Colonies left, and both players' decks have been clogged up with green cards and can no longer summon $8 or $11 to end the game on Provinces or Colonies. Usually then a race on Duchies (or Provinces) commences and sometimes the game ends up squeaking to a slow close on piles. However, this is basically just a failure case of the Province or Colony ending conditions. You don't need to worry a lot about this at the beginning of the game, and your strategy is likely to be similar to what it would be in a basic Province or Colony game.
Three Pile Depletion (Early/Mid game)
The rarest form of Dominion game ending is a rapid three pile depletion. These games can be very rewarding, as they are uncommon enough that many players miss the possibility of a rapid three pile depletion, and can be very unprepared for the game to end, allowing you to obtain a solid win.
In order for a rapid three pile depletion to be viable, there needs to be a way to deplete three piles quickly and for the player driving the game-end to do so with a safe enough VP lead that his opponent can't derail the strategy by buying a solitary Province or similar card.
The best-known board state for a rapid three-pile depletion is for both Gardens and Workshop (or Woodcutter) to appear on the board. Such a board typically ends with the depletion of Gardens, Workshop/Woodcutter, and Estates, and ends much faster than a Province game.
But any time you see one stack of cards that is almost certain to deplete itself rapidly, it is worthwhile to consider the possibility of a quick three-pile ending. The classic pile that is likely to deplete itself in the mid game is the Curses pile in the presence of strong cursing attacks, particularly Witch, Familiar, or Sea Hag (Torturers will probably only deplete the Curses in the late game if there are Villages on the board, or not at all otherwise; Mountebank often stalls out and doesn't deplete curses until fairly late because the attack can miss; Young Witch is often skippable or counterable, but if it isn't, it will cause Curse depletion). Popular, strong, spammable cards like Fishing Village and Caravan are also likely to deplete in the early game and can set up a three-pile ending. Grand Market is an interesting special case -- usually, it is expensive enough that it can't be depleted in the early game, but if there is something that starts a GM run early, it is so good at setting up other-pile depletion that it can very easily create a three-pile ending.
Duke/Duchy can also lead to a fairly early three-pile depletion.
If one pile looks likely to rapidly deplete itself, then a three-pile ending is much more likely than otherwise, and you should consider whether you can build a deck that will be substantially quicker than a Province/Colony deck and can take advantage of a three-pile ending. Typically, you'll need some way to deplete a VP pile (most likely Estates or a non-standard VP card) quickly without stalling out your deck. That will probably mean buying a lot of some enabler card that will be your third pile to deplete.
Conclusion
Understanding how a game will end is usually not particularly difficult. For most games, it can be reduced to "Colonies if Colonies are available, otherwise Provinces." Because of that, it's not heavily commented on here on Dominion Strategy. But despite being simple, it's crucial. You can't make a strategy for a board without understanding the pace of the board -- whether it's worthwhile to buy more expensive cards that will make your deck better in the long run, but slower in the first part of the game. And you can't understand the pace without knowing how the game will end.
Don't let yourself just assume that every game will end on Provinces or Colonies -- study the board before your game starts and look for the possibilities for a less-common ending condition. You'll save yourself several losses to people who end the game on three piles when your deck is just starting to kick into gear.