Each player has a certain number of cards in their hand. Each card has a casting cost that is shown in the upper middle of the card. If you have 7 cards in your hand you wont draw any more.
Here is an example of a card:
This is a Tree Mother. It is a Sylvan Creature.
Domain Level: This is what level of Domain you need to play the card. In this case you need to be level 3 Sylvan.
Flux Cost: This is how much flux it costs to play the card. The Tree Mother costs 5 Flux.
Keywords: These are words that might be referenced by other cards. This is a Treent. There could be some enchantment that gives all Treents +1 Vision for example. This would give this creature +1 Vision.
Special Action: Some permanents have special actions that you can take during your turn. This is just a description of what that action is. All special actions are preceded by ':'.
Special Action Cost: Special actions often cost something to perform. In this example the first icon means that performing the special action Dims the Tree Mother. It also costs you 3 flux. If a special action doesn't have the Dim icon that means you can perform the action multiple times even if the permanent is Dimmed.
The last things we will point out are the Figure's stats. Only Buildings and Creatures will have these. They are absent on other types of cards.
Attack: How much damage the figure does when it attacks, either by melee or shooting if it is a ranged Figure.
HP/Maximum HP: The top number is how many Hit Points or health the Figure currently has. If this is 0 or lower at the end of the round the Figure dies. The bottom number is the maximum HP the Figure can have.
Speed: This is how many spaces the Figure can move in a turn. Some terrain costs more to move across than others.
Vision: This is how many spaces the Figure can see. This is extra important for Buildings since where your buildings can see determines what part of the map you control.
Range: This is how far this Figure can shoot. It is often 0 except for Archers and other ranged Figures.
Most cards are listed in the wiki and may be found here.