The card types are artifact, creature, enchantment, instant, land, planeswalker, sorcery, and tribal. Of these, only instants and sorceries are nonpermanents; every other card type is a permanent. Also, every card type that is not a land is a spell.
Artifact is a type of permanent and may also be a creature, or an artifact creature. That means that anything that effects an artifact or a creature can be used on an artifact creature. So if you have Naturalize, you can use it on an artifact creature.
Creature is a type of permanent and will have one or other creature subtypes (e.g. Elf, Cat, Dragon, Wurm). All creatures have a power and a toughness and are the only card type that can attack or block. Some creatures have power and toughness depending on a certain thing, like Nightmare. Many creatures have abilities that boost their value and make them more powerful.
Land is a type of permanent and may have the subtype Forest, Island, Mountain, Plains, or Swamp. (There are other less common land subtypes.) A land may be played only once per turn and only by the active player (the player whose turn it is) on his or her turn.
Planeswalker is a type of permanent and may have one planeswalker subtype. All planeswalkers have a loyalty and three or four abilities that add or subtract loyalty. Only one of these abilities may be played per turn. Also, if two or more planeswalkers with the same planeswalker subtype are in play at the same time, they are all put into their owner's graveyard.
Tribal counts as a card Type because it allows cards like instants, sorceries, and enchantments to have creature types. (Goblin, Faerie, Merfolk, Eldrazi, etc.)
The Tribal type never appears on a card alone. It is always paired with another card type.
The type is unlikely to be used again except in very special circumstances.
Some permanents have the supertype legendary. There may be only one of any legendary permanent with the same name in play at any one time. If two or more legendary permanents with the same name are in play at the same time, they are all put into their owner's graveyard. This is known as the legend rule. (There is one exception to this rule when the card "Mirror Gallery" is in play)
Some permanents have the supertype snow. Any mana produced by a snow permanent is considered snow mana in addition to its color. Also, snow permanents may be subject to certain effects designated by other cards.
Some enchantments have the supertype world. If two or more world enchantments are in play at the same time, all except the most recent are put into their owner's graveyard. These no longer exist in the extended and standard formats.