1. At the start of every game evaluate which card is useful in which part of the game.

This part is usually about increasing your economic base and decreasing opponent's economic base.

Very useful cards are: most of Attack cards, Treasures and cards giving money. Usually you want only one Attack card of each present type (with some exeptions like when Attack is with +1 Action or there are too many Attack card types present).

Also you may want to gain some initiative by decreasing number of not very useful cards (like Estates and later Coppers) by trashing them (or exiling in Menagerie add-on). This is not so often of use, but however you can count your way. But remember that by adding Curses in your opponent deck you are decreasing his initative tempo.

That's why you usually shouldn't buy Victory Cards (except for useful ones) at the beginning.

You also can buy some Reaction cards (see part 2 of this Tutorial).

This part is about gaining power for card combinations and boost your economics. Treasures, +Actions-types, +Cards-types, some Attacks are useful. Remember that you want in total about 1:2 ratio for +1Action:+1Card features in your deck.

Usually when you can buy Province (or Colony), you should do that even before EndGame (with exception when you can buy Platinum). However, you should also build strong economic base. When opponent is buying Victory cards every round you (usually) should buy Victories or Treasures (if you cannot buy Victory card).

Beware of possibility of depleting 3 Supply decks. You can buy them and win (when exceeding your opponent by several points) or can lose when your opponent do so.

At the start of every game evaluate which card is the best response to which when played by your opponent.

Usually you want to decrease power of Attack cards of your opponent (by using Reaction cards or by using cards for decreasing negative effects). If he can add Curses in your deck consider buying cards for trashing or with +Cards ability.

Also you want to use your opponents actions. Some Reactions are good for boosting your economics and Durations are good for decreasing opponent's abilities.

Hard AI still can't use properly some cards (like Remake card in Dark Age add-on) and also sometimes can't calculate for long-period combinations.

Usually, 2 of Hard AIs gain power and try to compete with you. However, the 3rd one usually don't gain much power: he is just spoiling YOUR game. He will try to deplete 3rd supply deck, even Curses deck (while 2 other AIs will be overcoming you by several points), he will attack you when possible, and all of this while he won't have much Victory points. Beware.