user9339: How can you predict what your opponent will play in the next 5 turns, 7 turns, 10 turns?
If the game is like a tree, then the more the turns the more it will branch out.
How can a player accurately predict what their oppoent will play several moves into the future when the number of possible combinations of moves to get ten moves ahead can be ridiculously large?
Please give a detailed explanation.
How do I learn/acquire this skill?

user9030: Other answers are also good. But I would explain it simpler.
You just take account of few best moves, you don't care others because you know that they are inferior you can refute them easily. You keep calculating positions which are unclear for you, until you assess them. 
For example, if something lets you win a queen in a middlegame position, you know that is almost always winning for you(you assess it winning), and you stop calculating. 
Forcing moves let's you go deeper because if there are forcing moves it means there are less options(generally only one option, think about checks for example). 
So to conclude, it's generally easy get 5 moves deep, some positions lets you easily calculate 30 moves ahead, it really depends complexity of the position, and experience you have. Crucial thing is, who is calculating deeper and who is selecting candidate moves more correctly, that's the thing that decides the winner in a game.
Think Like a Grandmaster by Kotov is an excellent book which covers thinking processes in chess. I strongly recommend you to read this book.

user7314: I would recommend Dan Heisman for detailed explanations of how effective analysis is done in Chess.
http://www.danheisman.com/main_chess/chess.htm
Unfortunately, many of his articles have gone behind a membership wall now (at chesscafe.com), but not all:
https://www.chess.com/article/view/good-tactics-requires-analysis-and-pattern-recognition
To answer your question in short: you don't (predict 5,7,10 moves ahead); instead you find dangerous moves (of your opponent, then of your own) then look further ahead only on critical moves for stopping/minimizing the opponent's danger while maximizing your own danger.
(Note that in both of Dan's examples at the second link, you only need to "look ahead" at most 2 moves.)

user4362: The answer is that you only consider the most sensible and most critical options. This prunes the tree down to manageable proportions.
One easy example would be the fact that retreats are usually not threatening and therefore less likely to be critical. (Of course the downside is that actually dangerous retreats are often overlooked.)
To learn how to recognise potentially critical moves you have to play through master games, solve puzzles and play games. Over time your brain will store typical moves and manoeuvres in certain position. This ability is called pattern recognition. The more patterns your brain stores the stronger its intuitive move suggestions will be, you will be able to prune the tree more.
Another aspect is called "forcing moves". A forcing move is a move that requires a certain response, i.e. severely restricts the opponent's choices. For example checks, threats of checkmate and other kinds of strong threats. If your moves are very forcing the tree will resemble a path, because every step from this path is either illegal or results quickly in very bad things. If GMs calculate very long variations, these usually contain very forcing moves. In positions without forcing moves even the best players don't look very far ahead.
There is also a non-intuitve conscious part to "seeing ahead". Even if your brain provides you with only the most likely good moves, you still have to visualise the outcome of every variation in your head. That requires training as well, for example solving studies or tactical puzzles with long variations.

9339: <p>How can you predict what your opponent will play in the next 5 turns, 7 turns, 10 turns?</p>

<p>If the game is like a tree, then the more the turns the more it will branch out.</p>

<p>How can a player accurately predict what their oppoent will play several moves into the future when the number of possible combinations of moves to get ten moves ahead can be ridiculously large?</p>

<p>Please give a detailed explanation.</p>

<p>How do I learn/acquire this skill?</p>
 9030: <p>Other answers are also good. But I would explain it simpler.</p>

<p>You just take account of few best moves, you don't care others because you know that they are inferior you can refute them easily. You keep calculating positions which are unclear for you, until you assess them. </p>

<p>For example, if something lets you win a queen in a middlegame position, you know that is almost always winning for you(you assess it winning), and you stop calculating. </p>

<p>Forcing moves let's you go deeper because if there are forcing moves it means there are less options(generally only one option, think about checks for example). </p>

<p>So to conclude, it's generally easy get 5 moves deep, some positions lets you easily calculate 30 moves ahead, it really depends complexity of the position, and experience you have. Crucial thing is, who is calculating deeper and who is selecting candidate moves more correctly, that's the thing that decides the winner in a game.</p>

<p><a href="http://www.fellowshipabbey.org/files/Kotov,%20Alexander%20-%20Think%20Like%20a%20Grandmaster.pdf" rel="nofollow">Think Like a Grandmaster by Kotov</a> is an excellent book which covers thinking processes in chess. I strongly recommend you to read this book.</p>
 7314: <p>I would recommend Dan Heisman for detailed explanations of how effective analysis is done in Chess.</p>

<p><a href="http://www.danheisman.com/main_chess/chess.htm" rel="nofollow">http://www.danheisman.com/main_chess/chess.htm</a></p>

<p>Unfortunately, many of his articles have gone behind a membership wall now (at chesscafe.com), but not all:</p>

<p><a href="https://www.chess.com/article/view/good-tactics-requires-analysis-and-pattern-recognition" rel="nofollow">https://www.chess.com/article/view/good-tactics-requires-analysis-and-pattern-recognition</a></p>

<p>To answer your question in short: you don't (predict 5,7,10 moves ahead); instead you find dangerous moves (of your opponent, then of your own) then look further ahead only on critical moves for stopping/minimizing the opponent's danger while maximizing your own danger.</p>

<p>(Note that in both of Dan's examples at the second link, you only need to "look ahead" at most 2 moves.)</p>
 4362: <p>The answer is that you only consider the most sensible and most critical options. This prunes the tree down to manageable proportions.</p>

<p>One easy example would be the fact that retreats are usually not threatening and therefore less likely to be critical. (Of course the downside is that actually dangerous retreats are often overlooked.)</p>

<p>To learn how to recognise potentially critical moves you have to play through master games, solve puzzles and play games. Over time your brain will store typical moves and manoeuvres in certain position. This ability is called <a href="http://rads.stackoverflow.com/amzn/click/905691538X">pattern recognition</a>. The more patterns your brain stores the stronger its intuitive move suggestions will be, you will be able to prune the tree more.</p>

<p>Another aspect is called "forcing moves". A forcing move is a move that requires a certain response, i.e. severely restricts the opponent's choices. For example checks, threats of checkmate and other kinds of strong threats. If your moves are very forcing the tree will resemble a path, because every step from this path is either illegal or results quickly in very bad things. If GMs calculate very long variations, these usually contain very forcing moves. In positions without forcing moves even the best players don't look very far ahead.</p>

<p>There is also a non-intuitve conscious part to "seeing ahead". Even if your brain provides you with only the most likely good moves, you still have to visualise the outcome of every variation in your head. That requires training as well, for example <a href="https://en.wikipedia.org/wiki/Endgame_study">solving studies</a> or tactical puzzles with long variations.</p>
