I've seen too many variations of this answer and when put to practice, you really have to find the one that works best for your brain's learning behaviors. Here are three popular methods, of which #3 works better for me.
Method #1:
Step 1 : Blast through the moves without reading the annotations. Just play it over.
Step 2: Now re-play the game paying attention to the annotations for the played move, don't get lost in sub/side variations. That comes later.
Step 3: Finally re-play it one more time and go over each variation pain-stakingly.
Step 4: You should be able to play out the game without the notes/moves any more. This is a crucial step ... as it builds a muscle memory of the "types" of moves Masters tend to make.
Rinse and repeat. I would sometimes re-do step 4 the very next day to see how much of that game I still retained in my head.
Method #2: Basically a "light and rapid" variation of method #1
Step 1: Blast through the game, following only the moves; no annotations, notes or varations.
Step 2: Move over to the next game ... quickly!
Step 3: Once you've finished the book, repeat 1-2 or go to another game collection!
The rationale here (I've never tried it this way) from what I hear is that if you quickly play over TONS of instructive games, your brain starts sponging "master moves" by osmosis.
How does this help? Stronger players tend to have an innate feel about certain moves ... at my own club, I've seen a really strong player say "well, that move just doesn't look like it should be played in these types of positions". This "sense" comes from playing over tons of games ... where you get a feel for what are the moves that occur when pieces/pawns are placed in certain patterns.
Method #3:
Step 1: Figure out who won the game. Decide to play for that side.
Step 2 : Cover "your" own moves and read the opponent's moves and play it out.
Step 3 : When it's your turn, write down all possible candidates, reject all but one and write down why you rejected the rest + picked the one you liked.
Step 4: Now uncover the actual move and read the notes to figure out why it was played. Each time you and the Master played something different, you are learning some seriously good stuff if the annotations/author notes are instructive enough.
Step 5 : Sometimes the author does not indicate why he played what he did ... I usually save these positions and show it to a stronger player when I get the chance. They usually tell me why.
The advantage with this approach is that you are forcing yourself to think rather than just getting spoon-fed moves...though people might think that Method #3 is agonizingly slow. I think this works the best for me!
When people post questions about how best to improve at chess, the response is often that studying the games of Masters is a great tool. How are they best studied, though? I am a beginner (1050 or so on chess.com) and enjoy playing through the games in Chernev's "Logical Chess" and reading the notes. Is studying annotated games like this what people are referring to? What are some other ways to study them? Any recommendations on books? I do appreciate heavily annotated games. Thanks.