How are creature token cards used?
Can I summon a token?

No.

The "standard" way to cast a spell is to follow these steps (this is an extremely condensed version of comprehensive rule 601.2):


Take the card out of your hand and put it on the stack
Announce the spell (e.g., "I cast Elvish Mystic.")
Pay the costs of the spell


Tokens are not real Magic: the Gathering cards. They cannot exist in your hand. They do not have mana costs. You cannot add tokens to your deck. The rules simply do not allow you to cast them.

What are "tokens", exactly? 

Tokens are markers that represent permanents.


  110.5. Some effects put tokens onto the battlefield. A token is a marker used to represent any permanent that isn’t represented by a card.


How are tokens created?

It goes something like this:


You cast spells and activate abilities.
Spells and abilities create effects.
Effects create tokens.


What about those cards that come with booster packs that look kinda like real cards?

Those are tokens, and again, they are not real Magic: the Gathering cards. They exist only to give you, the player, something to use as a marker. They usually look like the thing they are representing, which makes them far more player-friendly than, for example, a die, or a piece of torn paper. You can't exactly turn a die sideways to show that it is tapped.