Ownership
Each player owns the cards he or she starts the game with. Whenever a card is sent to anyone's hand, library, or graveyard, it's sent to its owner's hand, library, or graveyard, as appropriate. Ownership of a card changes only when such a change is indicated on a card. Changing control of a permanent doesn't change who owns it.
Tokens
Certain effects put tokens into play. Tokens represent artifacts, creatures, and so on, and their characteristics are defined by the effects that create them. They can be cards, coins, bookmarks, or anything else; if possible, use something that reminds you what the token represents.
Tokens are treated exactly like any other permanent, except that they aren't cards. The color of a token is defined by the effect that created it and so isn't necessarily the same color as the effect. Since tokens were never spells, their casting cost is assumed to be (0). If a token enters play as a creature, its creature type is the same as its name. Each token is owned, and initially controlled, by the controller of the effect that generated it. If a token ever leaves play, it's permanently removed from the game; it can't return to play.
The effect on The Hive reads: "Put a Wasp token into play. Treat this token as a 1/1 artifact creature with flying." Therefore, once the token's put into play it becomes a 1/1 artifact creature that has flying. If it's put into the graveyard, it leaves the game, but any effects that look for creatures entering the graveyard, such as Creature Bond's take effect normally.
Counters
In Magic, some effects instruct players to add counters to certain permanents. Whenever this is the case, simply put the specified number of counters on the card. Coins, beads, or anything else that's handy can be used as counters. What you use to represent a counter isn't particularly important, so long as the card it's on is easily identifiable as having a counter. Counters generally serve one of two functions. First, they can be used to mark long-term changes to a permanent, such as giving a creature +1/+1 (not just until the end of the turn, but permanently). In this case, a single counter is placed on the card to remind the players of the change to that permanent. Second, counters are often used for "bookkeeping purposes." A card might enter play with counters or build them up for a while; its controller may then spend some or all of them to pay for an ability.
Bottomless Vault is a land you can choose not to untap as normal; if it's already tapped and you can decline to untap it, it gains a storage counter. It also has a mana-producing ability, which reads: "TAP: Remove any number of storage counters from Bottomless Vault. For each storage counter removed, add B to your mana pool." Therefore, you get B for each storage counter you remove from the Vault as you tap it.
Once a counter's been put on a permanent, it remains there until something specifically removes it or until the permanent itself is removed from play. A counter that has a continuous effect on a permanent is constantly applied to the permanent as long as the effect is relevant. If something happens to the permanent that makes the effect no longer applicable, the counter becomes dormant, waiting for its effect to become relevant again.
Mishra's Factory, a land, can become a 2/2 artifact creature for the rest of the turn. If it's given a +2/+2 counter while being a creature, the counter will remain on the Factory at the end of the turn, when it reverts to being just a land. If the Factory becomes a creature again, the counter will still be there, ready to give it +2/+2.
Counters that have the same name are considered interchangeable. For example, all effects that give a player poison counters say that a player with ten or more poison counters loses. Because these counters are all called the same thing, the source of a poison counter isn't important when checking whether a player loses. Also, all poison counters are considered the same for purposes of an effect that removes them.
Note that counters aren't tokens, and tokens aren't counters. Tokens are treated as permanents, while counters are used as markers or reminders that a permanent does something special.
Sacrifices
Certain spells and abilities require you to sacrifice a permanent, either as the cost for playing the spell or ability or as part of its effect. Also, effects often require a sacrifice as a penalty for something or as a cost to keep a permanent in play. A sacrificed permanent is always buried in its owner's graveyard. You can sacrifice only permanents that you control; whether you actually own them is unimportant.
A given permanent can't be sacrificed more than once. Thus, you can't sacrifice the same permanent to pay for two abilities or to pay for the same ability twice. If the spell or effect that called for the sacrifice is countered, you don't get back the permanent that was sacrificed. (See countering.)
Sources of Effects
Playing an ability follows the same procedure as playing a spell, with one exception. When you play a spell, the spell becomes the effect; modifying the spell changes what the effect does. When you play an ability, however, the effect that's produced is separate from its source. This means that if something changes or destroys the source, the effect is unchanged. As soon as an ability is played, its effect inherits all the characteristics of the source, such as color. The exact outcome of an effect depends on what's true of the source at the time the effect is played.
Bob uses his Brothers of Fire ability to deal 1 damage to Sue's Black Knight (and 1 damage to himself). As soon as the ability is played, the fact that it was generated by a red creature (Brothers of Fire) is locked into the effect. If Sue responds by changing the Brother's color to white, the effect is still red and the damage that results from the effect is still treated as having come from a red source. Even if Sue responds by killing the Brothers with Terror, this won't cancel the effect already played.