Mana pool and mana abilities
Mana is a resource stored in a so-called pool, which means players keep track of it, but it's not represented by anything usually (though players may choose to use counters for that purpose). It's important not to confuse lands, for example, with mana - they are permanents that produce mana in most cases, but they aren't mana themselves. Instead, they have abilities that produce mana, called mana abilities.
112.4. Some activated abilities and some triggered abilities are mana abilities. Mana abilities follow special rules: They don’t use the stack, and, under certain circumstances, a player can activate mana abilities even if he or she doesn’t have priority. See rule 605, "Mana Abilities."
Mana abilities can different in nature, and not all require you to tap the permanent to produce mana (such as Ashnod's Altar. However, most mana sources will simply give you a single mana if you tap the permanent producing it.
Basic Lands don't explicitly state what they do, but there's a rule defining their mana ability:
305.6. The basic land types are Plains, Island, Swamp, Mountain, and Forest. If an object uses the words "basic land type," it's referring to one of these subtypes. A land with a basic land type has the intrinsic ability "T: Add [mana symbol] to your mana pool," even if the text box doesn't actually contain that text or the object has no text box. For Plains, [mana symbol] is W; for Islands, U; for Swamps, B; for Mountains, R; and for Forests, G. (...)
Older versions of basic lands had a more obvious rendering, which helps to visualize the concept.
Using mana to cast spells
You can activate mana abilities any time you have priority, but also when a spell or effect requires you to pay mana, such as when you attempt to cast a spell. This means that there are two ways you can generally go about using mana to cast a spell:
- Announce the spell you're casting, and in the process of doing so, producing the required amounts of mana.
- Producing the required amounts of mana before doing anything else (known as "floating" mana), then announce to cast a spell and using the mana in your pool to pay for it.
The mana cost of a card indicates the mana you have to pay to cast it - nothing more. Once the creature is on the battlefield, it's mana cost becomes mostly irrelevant (other than for effects that care about it's converted mana cost or it's color, for example).
If you put the creature on the battlefield in other ways than casting it as a spell, you don't have to pay the mana cost either. If you cast Tooth and Nail, for example, you pay the cost of that card, while the creatures put onto the battlefield simply are put there by the effect.
Attacking with creatures
Though you do not usually have to pay a cost to attack with a creature, there are several requirements for you to be able to do so. For example, you must be able to tap a creature to declare it as an attacker, even for creatures that have Vigilance (which doesn't cause them to be tapped when attacking).
508.1a. The active player chooses which creatures that he or she controls, if any, will attack. The chosen creatures must be untapped, and each one must either have haste or have been controlled by the active player continuously since the turn began.
508.1f. The active player taps the chosen creatures. Tapping a creature when it’s declared as an attacker isn’t a cost; attacking simply causes creatures to become tapped.