How do you analyze master games? One of the pieces of advice (usually from masters) that I see over and over is that I should be analyzing master games. But how do I do that? 

Most of the tactics are over my head (obviously the simpler ones I can see). I can see strategical ideas all over the place, but my ideas are probably wrong. Without someone walking me through what to look at it's hard to understand. 

What should I be looking for? What should I look to learn?
It really depends on where your skill level is at. If you play rated Federation chess or happen to be buzzing around your favorite online server, you'd probably fall into a rating class or have a rating that serves as a great predictor of your skill/strength level.  

With that being said, here's a category-based answer to your question (using the USCF classes and typical online server ratings). 

( I'm only going up to class C as I'm currently a B player who's done his time climbing the ladder => is therefore somewhat qualified to make these recommendations :) )

USCF E (1000-1199) or 1200-1400 ICC/FICS with Slow Time Controls: 


Avoid just looking at Master games with no textual explanations.  There is ZERO value for somebody at your strength level. 
Avoid game books that contain no annotations/text descriptions for each move.
Avoid player game collections (e.g. My Best Games - Vishy Anand) and focus on the few Instructional + Annotated game collections out there.
Totally avoid any book containing games played AFTER the 1900s. 
Avoid game books that don't print out a diagram every 2-3 moves.
Always go over the game with a board or a computer.
A lot of these books mean well but often drown you in a ton of variations. It is fine to skip over this part and just get to the move that was played! :)
If you are using a computer, keep the engine off. You don't need it at your current strength level.
Get used to covering up the next move and playing "guess the move". You'll want to do this for every game you ever look at going forward.
Pay attention to the opening PRINCIPLES, don't even dare try to memorize openings or worry about the nuances. It really doesn't matter at this stage ... the principles alone are sufficient.
Write things down on paper or use a database application. The minute something feels vague or does not make complete sense to you, write down your question. Don't immediately read the author's explanation. Come up with your best answer. Then .. and only THEN read the text. You'll be able build a great foundation and start thinking for yourself. It will also boost your confidence when your own ideas are in sync with what was played.
Go back to this game a week later  and review it again. It should feel like a grocery store you've visited in another city a year or so ago. You'll feel comfortable but not enough to not notice something or find a new question worth asking.  Review your previously asked questions ... do the answers now seem obvious? If so, you're making progress!
Finally : Always find a strong-er player or ask a credible forum about a position that stumps you. Even some well written instructional books may not completely explain why a certain move was played in a given position.


Recommended Books: A First book of Morphy (Rosario), Chess Master vs. Chess Amateur (Euwe)

USCF D (1200-1399) or around 1400-1600 ICC/FICS with Slow Time Controls: 
Same as above, except now:


You can and should use a computer engine to look at other tactical possibilities that the book did not go over.
You can start looking at pre-1950s games, but still avoid contemporary games/the modern era. 
Practice finishing off the game vs. a computer from the position at which one of the Masters resigned. For fun, try to win it at blitz time controls! If this is becoming a struggle, seek help from a stronger player to show you the correct technique (which was bloomingly obvious for the Master who resigned :)) 
There are some very famous games in chess history that every "Russian schoolboy" knows. Google them out and play through them. 


Recommended Books: Chernev's Logical Chess and his Most Instructional Games of Chess.

USCF C (1400-1599) or around 1600-1800 ICC/FICS with Slow Time Controls: 


Same as above, but you can finally start poking around at what the big boys of modern chess are doing.  You still want to read books that are intended to be instructional, not just a showcase of somebody's favorite games.
You should have a set of pet openings (repertoire). Seeking out games of Masters who play your opening makes sense.
Make sure you now work through the variations those books tend to spit out. They are quite insightful and show you how much calculation is often needed in critical positions.
Focus on players who often play very natural and beautifully elegant games without tons of complexity. (Capablanca, Fischer would be good examples)
Start focusing on the endgame aspect of their games. Especially how the winner strategically transitions into the endgame he WANTS, making the correct piece trades at the right time.


Recommended Books: Weeramantry's Best Lessons of a Chess Coach.