Here are some basic strategies for Dominion.

Big Money

Buy the best treasure you can afford each turn, or a Province. This is a basic strategy that will not win you many games, unless you’re playing against new players.

1-2: No buy
3-5: Buy silver
6-7: Buy gold
8+: Buy Province

Grand Smithy

Buy Smithy until you have 3 of them. Otherwise, buy the best treasure you can afford, or a Province. This will always beat Big Money, because Smithy is usually a much better buy at 4-5 coins than silver.

1-2: No buy
3: Buy Silver
4-5: Buy Smithy, limit 3
6-7: Buy Gold
8+: Buy Province

Chapel Strategy

For turns 1 and 2, buy Chapel and Silver. After that, chapel away all coppers and estates you draw, while buying silvers and easing into another strategy, usually buying treasures and +card draw.

Turbo Remodel

This strategy means forgoing most card buys other than Remodel. When you start out, getting a Silver and a Remodel are optimal buys. Then,make the following Remodels:

Estate -> Remodel
Remodel -> Gold
Gold -> Province (Once the game is close to ending, unless you can use the Gold to buy a Province that turn)

Good support cards include Cellar, Throne Room, Village, and Chapel, which all make your Remodels more reliable and more frequent.

Other Tips

Don’t buy too many actions that don’t themselves give +actions. Otherwise you’re at risk for drawing multiple actions when you can only play one of them.

When players start buying Provinces, carefully take note of how many each player has bought, and how many are left. Once there are about 1-2 provinces left per player, it’s time to stop buying cards that don’t give you +Victory, because there won’t be enough time to draw any new cards you buy.