The cliff notes version of this article is simply this: think about what cards your opponent has in hand. As always, though, the devil is in the details.
You can logically work through what your opponent is most likely holding based on his play. Eliminate possibilities by thinking through how your opponent would have played the game if he had the card. Did he have an opportunity where you would have expected him to play the card if he had it, but he did not? Have his plays been consistent with having the card? For example, say your opponent on the play curves out Goldmeadow Stalwart, Knight of Meadowgrain, Wizened Cenn with Plains up, to your turn one Lightning Bolt on Knight, turn two Putrid Leech. If he doesn't attack his Stalwart into your Putrid Leech on turn three, then his play is inconsistent with Harm's Way and you can assume he does not have it. Similarly work through what is most likely in your opponent's grip by thinking through what spells he has not had a chance to cast. If you haven't presented any must-kill targets for removal, it isn't hard to guess what your draft opponent is sitting on in a stalled game.
If your opponent deviates from routine play, what makes his play correct? There is typically a small set of possibilities that can explain unusual play. The classic example here is someone playing super defensively in Limited, choosing not to race when it is seemingly highly favorable for him to do so. This play tells you that he thinks he has inevitability. If a RW drafter is playing like this, brace yourself for the coming Chandra / Siege-Gang Commander / Baneslayer Angel. If your opponent willingly enters a seemingly unfavorable race, you can count on him having something to swing the race in his favor, such as an Overrun, Sleep, or burn. Is your opponent actively avoiding trading? Again, they are probably trying to Overrun or Sleep you out.
One of the most useful things to think about is what hand your opponent kept. Especially when they have a seemingly poor draw, you want to figure out what would make them keep the hand. If you are playing a deck like Time Sieve or Sanity Grinding against Jund and your opponent keeps at seven cards and doesn't have a very aggressive start, you can pretty reliably expect Thought Hemorrhage. In the Faeries mirror if your opponent is on the play and doesn't play a spell on their first two turns, it is very likely they have a Broken Ambitions. Kithkin against 5cc and they don't have any cheaper spells like Plumeveil or Lightning Bolt to keep up with you? You know they have a sweeper. Why else would they keep?
Players give away all kinds of free information about their hand, if you pay attention. Personally, I don't put much value on "reading" opponents through their behavior, but I'm also really bad at it so I'm not going to pretend that it isn't much more useful for others. There is, however, one "tell" that I find incredibly and universally useful (even online!) - when players stop to think. A player stopping to think through a play, assuming that is actually what he is stopping for, provides great insight into his hand. You simply need to ask yourself what your opponent is thinking about.
If you are with Fae on the draw and have turn two Bitterblossom, and your Jund opponent tanks on his third turn before playing Boggart Ram-Gang, there's not many cards he could have that would give him a real decision there. Maelstrom Pulse is the most likely candidate.
If you play a turn two Runeclaw Bear and your opponent pauses momentarily end of turn with a Mountain in play, it's pretty obvious what is going on. Likewise if you attack Stormfront Pegasus into an open Island and Plains and your opponent stops to think; Harm's Way is the only spell they could realistically be thinking about casting.
If you are sitting on the other side of the table, you should already have thought through whether you would Lightning Bolt a Bear, or Harm's Way the Pegasus, as pausing too easily tips your hand. Think on your turn how you would respond to various plays from your opponent, what you would counter and what you would spend removal on.
Equally as important as paying attention to when your opponent is thinking is noticing when he is not thinking. If he is blazing through every turn, he probably doesn't have very many options, and you should take note of that. Most Blue mages are good about pausing even for spells they know are resolving, but if your Islands-wielding opponent doesn't even consider countering a relevant spell, it can clue you in to the coast being clear. Playing a deck like Faeries, you want to get in the habit of thinking on your own turn even when there is no chance you will do anything other than pass the turn. You should be able to plan how you will play on your opponent's turn, figuring out what you will counter, how you will block, etc. If you aren't in the habit of doing this, then when you have to stop on your turn to think about upkeeping Mistbind or playing Jace or whatever, you give away too much information.
For many players, there is a discernable difference between them legitimately thinking through something, and them merely pausing. This is both something to look for in opponents, and something to be careful you aren't guilty of yourself. The easiest remedy to this is to actually think about something when you pause. Think through how that spell affects the game before letting it resolve, think about your outs when you peel that land, think about Vegas and the Mirage if you must, just don't spend that time durdling.
Realistically, you are always going to be playing with imperfect information on your opponent's hand, and the real trick is how to deal with that imperfect information. An especially useful tool is to to make assumptions about your opponent's hand based on what you can and can't beat.
When you are ahead, figure out how you would most likely lose the game and what your opponent is going to need to beat you, and assume that they have it. If you assume the worst, and play to beat it, and your opponent ends up having a weaker hand, it's probably irrelevant that your play was not optimal given what they had.
If you are in a dominant position with Faeries against say Reveillark, ahead on the board with some counterspells in hand along with Mistbind, it is rarely correct to upkeep the Mistbind. You are highly unlikely to lose the game from this position, unless you were to do something like run your Mistbind into Path and allow your opponent to resolve a key spell. You should assume the worst, Path plus Reveillark, and play to beat it anyway by sitting on Mistbind. If your opponent doesn't end up having Path, you don't crush him nearly as mercilessly, but that doesn't matter as you are still in a nearly unloseable position.
Putting the Read into practice
At the most recent Superstars 5k, in a game against Merfolk with 5-CC, my opponent had a couple of fish and I had a Wall of Reverence in play and just resolved Baneslayer Angel into untapped mana. End of turn, Wall of Reverence targeted itself rather than the Baneslayer, and Baneslayer was met with a Path to Exile. It's not that I had a sick read on Path, it's that my opponent was just dead if he did not have it, and missing four points of life gain would be irrelevant. My opponent had to have Path to be in the game, so I played like he had it.
Similarly, if you are behind figure out what you can beat your opponent having, and assume that is all he has. It's irrelevant if you play right into his spells and get blown out, as you weren't going to win the game regardless. Know what you aren't going to be able to beat, and don't try to play around it.
Sometimes you have to run that upkeep Mistbind with just a Sprite in play and pray. It may look embarrassing when your opponent bends you over with a Fallout or Lightning Bolt, but if you couldn't beat those no matter how you played, it was still the correct play.
At the 5k I witnessed a 5-CC mirror where one player had Great Sable Stag in play to his opponent's nothing, both with about ten lands in play. The Stag player had a couple of [card]Negate[/card]s and lands in hand, and his opponent had four cards. The opponent cast Ajani Vengeant, and the Stag player let it resolve. He was worried his opponent would have two spells more important to Negate, like Cryptic and Cruel Ultimatum, but he wasn't in a strong enough position to play around those. Allowing the Ajani left him behind no matter what his opponent had, as he now had an Ajani he would eventually have to deal with. If his opponent did in fact have two spells better than Ajani, the Stag player is a pretty big underdog even allowing Ajani; he probably wasn't beating two spells more important than Ajani. He should have played assuming his opponent did not have them, and Negated the Ajani.
So, think about what your opponent has in hand, and do what you can to glean information about what they are holding. But also recognize what your opponent needs to have, or what you need them to have, as often it's just as good to play to what you can beat as it is to play to what your opponent actually has.
(Hmm, Josh wrote a conclusion this time. Well, that never stopped me before! - LSV)
Figuring out what to play around is a pretty tricky proposition. Play around too much, and you might lose the advantage you hold by giving them too much time. Play around too little, well, and you lose to the cards you should have been playing around. Alternately, you could use LSV's plan, which is always "assume they have nothing". Sadly, it seems to keep working for him, making an utter mockery of the laws of probability.