You won't usually have any tapped cards until you have already played a couple turns of the game. The following rules talk about the order in which things happen.
The level for a creature is in the upper left corner. You can play these cards in any order.
Tell your opponent that you're done with your turn. Choose one, have it attack, choose another one, have that one attack, and so on. Start a Wiki. You can use one of your "blocker" creatures to stop any attack. Creatures with Double Breaker can break more than one shield when they attack your opponent.
If the powers are the same, put both creatures in their owners' discard piles. Choose a spell from your hand.
If one creature's power is lower, put it in its owner's discard pile. Now it's your opponent's turn! So, for a level 5 Water spell, if you had one Water card and 5 Fire cards in your mana zone, you could tap all 5 Fire cards and cast the spell.
Each creature has a power number in its lower left corner. Next, you must tap cards in your mana zone equal to the spell's level.
If you can't pay for the cards level, you can't summon the creature. The creature with the higher power wins the battle. Only the person who plays first skips drawing a card on his first turn.
You can put only 1 card of any type into your mana zone from your hand each turn, unless a spell or effect allows you to put more. When you want one of your creatures to attack, choose which creature you want to attack with, tap it, and choose what it's attacking. As many of your creatures as you want can attack each turn.