Reading your opponent's strategy

"Know yourself but not your enemy and you will lose as often as you win."
-Sun Tzu

So Sildani on the Warseer boards asked "Do you find yourself anticipating your opponent's moves, a turn or two in advance?... Basically, I'd like to know how you became so tactically astute so I can similarly elevate my game. And yes, I've read Sun Tzu and Clausewitz and have applied them, so at least I can say I've won more than I've lost."

My answer, with some updates:
Thinking ahead a turn or two is certainly a vital skill to learn. If you can discern your opponent's tactics for the next turn, you'll certainly be at an advantage to winning games. A tank can sit a bit farther into cover, a unit can back off a touch in hopes that Difficult Terrain tests trip up Assaulters, etc... Little things like this allow you to lever numerous small advantages that can tip the game in your favor.
But to dominate games consistently, you need to understand and plan for the entire game from beginning to end. This doesn't mean you should try to crunch the odds of every single possible move and attack... that's for computers, autists and savants. I'm talking about understanding their game plan; their strategy. If you can grasp that, not only will their tactical choices become easily predictable, but you can manipulate their own strategy to your benefit.
Figuring out someone's strategy can be a bit daunting. I don't follow a set pattern, but a crude version using the 5 basics of writing would be:
1. Who are they? Typically easiest with a regular group, as you know each other, who plays how, what their confidence level is, etc. Are they the type to play for the win, play for the kill, play by the statistics, or play for fun/story?
2. What are they fielding? It is critical to take a minute before you start and read your opponent's army list. The unit selection, weaponry, balance and overall composition can be a HUGE insight into their strategy and how they play. A large part of doing this effectively is having done your research before-hand.
3. When are they going to try ploys or grab objectives? Example: Objective capturing. Some armies Infiltrate and camp objectives from the start, others will advance onto them in a wall of iron mid-game, and others will just ignore them to jump back on them at the endgame. When you understand the timing of their list, you can understand when you need to be on guard versus when you can attack unimpeded.
4. Where are they going to focus? Locate the key points of the field (firelanes, hardpoints, objectives, etc) and then think of what would concern your opponent and their list. Also look at your list from their point of view and locate the concerns there. Might they avoid a courtyard if there's a unit of Reapers at the end? Is it worth putting the Reapers there anyways to keep him from flanking your gunline? Would adding an objective or sacrificial unit there tempt a squad to walk into the Reaper's killing zone?
5. How are they going to do unto you? This is where you add together all of the above. Try to envision what their overall strategy at the start of the game and how it adapts to the game. Even just a basic sense of their plan can be enough to take control of the game.
Let's take an example from my first Ard Boyz game. I don't think I'd ever played Chris before this, but he wasn't a complete stranger either. We'd chatted tactics and seen the other at prior tournies and just never faced off. I knew right off from this that he was an aggressive player who'd go for the throat if it was offered, but also smart enough to remember the objectives and play for the win. Looking at his list, I saw an aggressive list with some decent mobility. His defensive units were good versus range, but would suffer against CC, flamers or out of cover. They relied on the mechanized line to hold the opponent away. His aggressors were hella scary at close range, but ignorable at long. This made me bet that he'd go for an aggressive armoured push that tried to hit my lines at the same time or at least as a one-two punch.
So with this in mind, I placed my objectives and Wraith units all central. This was a solid a block of durable Troops sitting on/near 3 objectives. He couldn't just ignore them and would require something strong to dislodge them. I figured this would be his Sternguard and Termies, plus maybe a Dread or two. The thing is, it didn't matter to my strategy if my center held or fell. The key was to get him to commit a massive force centrally. This allowed my speedy units to run the edges, take out his defensive Scoring units, and still be in position to jump in and grab/contest objectives at leisure.
But this was only if he chose to follow the most tempting and likely strategy. I also made secondary plans for him pushing his forces to one side, splitting up and going for my flank, or just sitting back and waiting for me to come to him.

Said another way, the specific targets and even the results of what his Land Raider chose to shoot while advancing were incidental. That the Land Raider was going to advance to place the Termies seems obvious, but is still crucial to know and not definitive. But deliberately placing my objectives and army such that I was able to guide his strategy, causing the Land Raider to go for the center? That's how I took control of the game and won.

My #1 piece of advice for players looking to up their game? Talk to your opponent. After the game, grab a beer/soda/water and chat about what worked and what didn't for both of you. Post-game debrief is the most useful and informative tool. Talk about what their strategy was and why they chose what they did, then compare that to what you expected them to do. Also discuss what could have gone different and any mistakes made. Be fair and objective about things and you'll get some excellent feedback. It can also key you off to ploys or stratagems they might try next time. For example, I chatted with Chris afterwards and found out he'd realized he'd been snookered in my Turn 3, but didn't have the position or mobility to regroup. His comment was "I won't fall for that one again..." So now I know I won't be able to get away with this same plan next time. Maybe I'll try a swapped or refused flank instead. :-p

Anyways, I hope you have all found this useful or at least interesting. Cheers and good hunting!