A 'limited' format refers to a type of game you play with a limited card pool - so rather than picking and choosing the cards you want from everything available, you are given a set amount of sealed product to construct your deck out of.
There are three main limited formats:
Sealed
To play Sealed format, you require six sealed booster packs per player. Each player opens their booster packs, puts the loot, crafting and hero cards to one side, and constructs a minimum 30-card deck out of the remainder of the cards they opened; this follows all normal deckbuilding restrictions.
You can use any hero from any of the sets you are playing with - you do not have to build a deck that fits the heroes you opened. Half an hour to an hour is usually given for deckbuilding purposes.
Once all decks are complete, swiss rounds are played depending on participants (usually three rounds if below eight players, and four rounds with 8-15). You can also cut to top 2/4/8 though this is not widely done in the UK other than at larger tournaments.
Draft
A draft 'pod' consists of between four to eight people. Players require three booster packs each. Players follow the below method to pick cards to enable them to build a minimum 30-card deck. The deck must follow all normal deckbuilding rules, and can use any hero from the sets you are drafting - you do not have to open the hero you wish to use.
The players should sit around a table in a circle and when everyone is ready, all players open the first pack simultaneously. Loot, crafting and hero cards are all removed from the pack, and then each player removes one card from the pack they have just opened, places it face down in front of them, and passes it to the person on their left. What you pick is secret; you should not reveal this at any point during the draft.
Depending on how serious the draft is, there will either be a judge or TO (Tournament Organiser) calling 'draft timings' - for the first couple of picks you will have 60 seconds to choose your card, then the amount of time per pick starts to decrease as the number of cards you are passed does.
Obviously, as all players are sat around a table, you will receive cards from the person on your right. Count the cards to ensure that nobody has picked more than one card, then pick a card for yourself. Pass the pack to your left, and keep picking until you are passed a single card from your right.
At this point you are given 60 seconds to review what cards you have picked so far. While you are in the process of drafting, you should not look at the cards you have taken other than in these allotted windows of time.
Once this time is up, all players open the second pack, remove all crafting/loot/hero cards, pick a card using the same rules above, then pass to their right. The third pack is opened after the second is empty and there has been another 60-second review, and this is passed to the left, like the first pack.
At the end of a draft you should have 54 cards, and after you have built a minimum 30-card deck with these, you will play three rounds of swiss pairings to determine a winner.
If, for instance, you have 16 players for a draft, you should seperate them in to two eight-man pods, who will draft independently; the two pods should then play three rounds of swiss pairings playing only opponents from their pod, and then the top two finishers from each pod should play a top 4 knockout to determine the overall winner.
Two-pack
Two-pack is not quite such a serious format as the above two - it's a good laugh to play when you are opening boxes of a new set, and is also sometimes used in League Play at Darkmoon Faire events.
Generally two-pack is played 1v1; each player requires two sealed booster packs. They should be opened face-down so neither player can see the contents of the cards; crafting, loot and hero cards should be removed. Crafting and hero cards have art on the reverse; if the hero card is missing then you have a loot card! Run your finger on the printed side of the cards either side of the crafting card; you are looking for the scratch-off panel that all loot cards carry.
Combine the two booster packs and shuffle them face-down without looking at the printed side of the cards. Pick one of the heroes that you opened in your two packs - this will become your hero for this game.
After this, follow normal game procedure - every card that you opened in those two packs is legal in your deck, even if your hero is of a different class or faction.