This is going to be a lengthy answer, but it will be that way because I have to explain how the stack works.
The "stack" is an invisible object that bounces "priority" back from one player to another. For example: I tap my forest for mana, and cast a Lanowar Elves, at that point, my Elves go onto the stack and "priority" is shifted to my opponent, at which time he can choose to play an instant or a card with flash. Should he choose not to, my Elves then go into "resolving" status and then come onto the battlefield. As spells are resolving on the stack, no other action may be taken by either player until the stack is once again empty.
Here is a different scenario: I again cast my Lanowar Elves, at which time they go onto the stack, my opponent plays a Cancel, which goes onto the stack as well, but over top of my Elves, since it was added to the stack after I cast my spell. The stack resolves from the top down, meaning, that my opponent's Cancel would be resolved before my Elves, which in turn means that as the target of the Cancel, my elves would be countered.
The stack starts to get tricky when you factor in activated and triggered abilities. Here is an example: I tap my Prodigal Sorcerer to deal one damage to my opponent. The ability is put onto the stack, at which point my opponent may act. My opponent then taps his Icy Manipulator in response to tap my Sorcerer. This is an illegal move. Since my Sorcerer was tapped to activate its ability and the ability was put onto the stack, the Manipulator cannot be tapped in response to tap my Sorcerer. Once the ability hits the stack the card is tapped.
Triggered abilities are a little bit different however, say my opponent just killed off my Nether Traitor which triggered the ability of another Nether Traitor in my graveyard. My opponent at that point could play a card that allowed him to negate that ability since priority has not shifted back to me at that point.
When you play Hypergenesis (HG), it goes onto the stack, at which point your opponent is allowed to play an instant or an interrupt. If he/she chooses not to then HG "resolves" what that means is that the spell effect is triggered, which allows you to "put a artifact, creature, enchantment, or land card onto the battlefield". This is different than casting, if a spell effect allows you to put something onto the battlefield, it cannot be countered. You can only counter a spell that was "cast". Nothing that comes into play from HG was cast, so therefore cannot be countered. Furthermore, since there is a spell on the stack that is still "resolving" no one, either you or your opponent can play any other spells, so you cannot play a sorcery instead, so no your opponent cannot Cancel that sorcery. You would have to wait until HG has finished resolving (i.e. both you and your opponent did not put a card onto the battlefield) before any other action can be taken. You can put your Iona, Shield of Emeria onto the battlefield and there is nothing that your opponent can do about it.
If you have any other questions you should check out the Official Rule book at http://www.wizards.com/Magic/TCG/Article.aspx?x=magic/rules
I do have to warn you however, the rule book is extremely large and hard to understand at times. Have fun playing Magic though, its a sweet game.