1. The active player is the player who has priority. Depending on the phase, the active player can play one or more of the following: instant, sorcery, planeswalkers, creatures, lands and / or artifacts.
Lands do not use the stack and cannot be countered. All other spells use the stack. When a spell is played, it is announced. That spell cannot resolve until the active player passes priority to their opponent. The active player does not have to pass priority immediately and can play additional spells while they have priority; however, none will resolve until both players have had a chance to act.
Once priority is passed, the opponent becomes the active player and may play 'instant' spells, or spells that read 'can be played as an instant' within their card text.
At that point, a counter spell may be announced and paid for through mana, along with a target spell to be countered. The active player, in this case the opponent, then must pass priority back to the original player, at which time, they too get to respond with their own actions. If they do respond, priority is passed back again. If they do not respond, the spells resolve in the order in which they were played, also referred to as 'the stack'.
As spells on the stack resolve, other responses may be made.
The short answer: They play a spell. You then play the counterspell, targeting that spell. If they don't have a response, such as countering your counterspell, then the spell fizzles.
2. Any type of control deck involves restricting your opponent from using their strategy to win the game. This involves playing 'answers' to your opponents 'threats'. In order to do this effectively, a control player must gain the advantage in other areas of the game, because if you don't, eventually your opponent will play one to many threats, and you will lose.
The most effective control strategies involve card advantage. It is probably the single most important aspect of building a competitive control deck.
Generally, all control decks play counterspells and mass removal spells, but card advantage is where the real control comes from.
Examples:
1. If an opponent plays three creatures and you play 'Wrath of God', that player loses three cards and you only lose one card, netting you a card advantage of +2.
2. If at the end of an opponents turn, you can play a card that will allow you to draw two cards, then that nets you +1 card advantage.
3. If you can put a card in play that causes your opponent to discard a card each turn, you will net +1 card for every card after one.
As for creatures, there are many different strategies. Some control decks will only play a very small number of creatures, preferring to play card draw and counterspells first-and-foremost. Then, the creature that is finally played toward the end of the game is usually so powerful that it locks down the opponent by simply being in-play.
Another strategy is to use creatures with triggers, such as discard and card drawing triggers, allowing you to gain card advantage and overwhelm your opponent. Another strategy is to use creatures that are constantly recurring from the graveyard, and is yet another effective form of gaining card advantage.
Creatures that can be played as instants are especially effective, because you can avoid tapping your land on your turn in favor of counterspells, and if your opponent does not play a threat on their turn, you can play your 'instant' creature at the end of their turn. Then on your next turn, that creature does not suffer summon sickness and you lands are untapped again allowing you to protect that creature from leaving play.
Another highly effective creature for control decks are those that act as counterspells themselves, such as 'Mystic Snake' or those that giver other creatures 'Shroud' when played as instants. These types of creatures allow you to generally put a creat