1.
When you look at the games of club players, you often see draws agreed in positions which are clearly better for one side, e.g.:
Blackmore  Isaac (116) (3), 1995

Move chosen: draw agreed
Better move(s): 33...c4
Commentary:
Black has generally better pieces and two Bishops, while White has little play. If you look around the position there are lots of little ideas for Black (...Rb3, ...Be2) and few for White. The pawn move suggested gives the Black Knight a superb post and releases the Bishop on e7. I don't mean to pick on Mark, I've done the same myself (more than once!), but the point must be made.2.
When you read books about Capablanca, you read comments like:
"Whether this advantage is decisive or not does not interest Capablanca. He simply wins the ending! That's why he is Capablanca!"  EUWE
Can we become more like Capablanca?
Most people would say no, because Capa is a genius, with almost faultless insight into the theory of endgames. But you don't need to be a genius to win drawn endgames. Have a look at this one from "Chess for Tigers":
Miles,AJ  Webb,S (Birmingham) 1975
(wKg2,Qd4,Rb1,d1,Pa2,f2,g3,h2; bKg7,Qf5,Rc8,f7,Pa7,f6,g6,h7)

23... Rc2 24. a3 Qc5 25. Rb3 Qxd4?
Simplifying but going on the defensive  a needless concession.
[25... Re7]
[25... Rc7 26. Rf3 Qc6]
26. Rxd4 Re7 27. Ra4 Kf7 28. Ra6
White has contrived a little threat, which costs nothing, and Black might be careless...
28... Rce2 29. Rb4
[29. Rf3 R2e6]
29... Rd7 30. Rba4 Ree7 31. g4! h5?
Creating targets on the King'sside  another concession. Holding tight would have allowed a weakened square on f6 but White has no way through.
[31... Kg7 32. h4 Kf7 33. g5 fxg5 34. hxg5 Kg7 35. Rf6]
32. gxh5 gxh5 33. R4a5 Kg6 34. h4

34... Rc7? Careless.
[34... Rf7]
35. Rg5+ Kf7 36. Rxh5 Kg7
Now it's lost. The technical phase may give White problems, but that's not the point: Black should never have lost the Pawn.
37. Rf5 Rf7 38. Kg3 Rc3+ 39. f3 Rc1 40. Rfa5 Rcc7 41. Kg4 Rc4+ 42. f4 Rcc7 43. Kf5 Rb7 44. a4 Rbc7 45. h5 Rb7 46. h6+ Kxh6 47. Rxf6+ Kg7 48. Rxf7+ Kxf7 49. Ra6 Rc7 50. Kg5 Kg7 51. f5 Rd7 52. a5 Rc7 53. Rd6 Kf8 54. Rd8+ Ke7 55. Rh8 Kd6 56. Kg6 Rc1 57. Ra8 Ke5 58. Re8+ Kf4 59. f6 Rg1+ 60. Kf7 Ra1 61. Kg7 Kf5 62. f7 Rg1+ 63. Kf8 Kg6 64. Re6+ 10
What's going on here? It's not chess theory or insight, but psychology.
White was playing as though he was going to win. He kept trying to put pressure on the opponent, collecting little advantages, looking for opportunities.
Black was playing as thought he was trying to draw. In fact, he tried and failed. He kept solid, but passive, and kept making little concessions  and the biggest concession really was his attitude.
Black should have been playing much more assertively, not thinking about the result, but the position, trying to play the strongest and most active moves, making concessions only when forced to. In fact, it is said in truth that the best way to draw is to play for a win. Not in a reckless way that Tarrasch wryly termed "playing for the loss", but rather like Miles did  keep playing actively  and not like Webb did  don't give an inch that you aren't forced to.
Once we have realised this, we can see it in other games:
Cooper  Hebden (Lutterworth) 1986
(wKg1,Qf4,Rf2,Pa2,b2,g2,h2; bKg8,Qe6,Rf8,Pa7,f7,g7,h6)

1. b3 Rd8 2. Qf3 Rc8 3. g3 Rc1+ 4. Kg2 Re1 5. Qa8+ Kh7 6. Qf3
[6. Qxa7 Qe4+]
6... Kg6 7. Qd3+ f5 8. Qf3
White is just hacking about, perhaps thinking vaguely about perpetual check, waiting for the draw to turn up. These hopeful checks are actually timewasters, and hope gradually fades...
8... Re3 9. Qb7 Kh7 10. Rf3 Re1 11. Rf2 h5 12. Qf3 g6 13. Qb7+ Kh6 14. Qf3

14... Re4 15. Qc3 g5 16. Qh8+ Kg6 17. Qc3 Qd5 18. Kg1 h4 19. Qd2 Rd4 20. Qe2 Rd1+ 21. Rf1 Qd4+

22. Kh1
[22. Qf2 Qxf2+ 23. Kxf2 Rd2+ loses a Pawn, but that may have been the best chance.]
22... Qd5+ 23. Kg1 Rd2

24. Qe8+ Kg7 25. Qe7+ Kh6 26. Qf6+ Kh5 27. Qh8+ Kg4 28. Rf4+ gxf4 29. Qxh4+ Kf3 30. Qxf4+ Ke2 31. Qf1+ Ke3 32. Qf4+ Kd3 01
And, if you will forgive the immodesty, once you have seen this done, you can even imitate it.
Wilcox, RJ (154)  Regis, D (168) (Paignton #3) 1996

40. b4 Re4
Time control, and I offered a draw. Declined! So, Black must fight like fury. Activity is everything, going passive is equivalent to resigning.
41. b5
[41. Rf1]
41... Qd3 42. Qa2

42... Re2 (Sealed)
43. Qa8+?
This "hopeful check" actually just exposes the Rook.
43...Kh7 44. Rf1 Re7
White obviously hoped Rf1 was strong; he and his colleagues had overlooked Black's best reply. This can be seen as a simple oversight, but also as reward for Black using his pieces as actively as possible.
45. Qf3 Qxb5 46. Qf6=
OK, we have have now a new phase. This is objectively a drawn position, I believe. I thought this at the time, but was happy to play on, knowing that White had to adjust his mood to suit the new situation. I had the example of the MilesWebb game very much in my mind while playing.
46...Qe2 47. Ra1 Qe6! 48. Qd4
[48. Qxe6 fxe6 obtaining a passed Pawn is very much what I hoped for]
48... Qe5!? (bluff)
49. Qa4?
[49. Qxe5 Rxe5 50. Ra7= is absolutely level. Normally you try to keep pieces on when trying to draw, but while Black has an extra Pawn, with Pawns on only one side, it's a draw. White should have known this.]
49... Qd5 50. Rf1?
Passive. [50. Rd1]
50... Re2 51. Rg1 Re3 52. Kh2 Qe5+ 53. Kh1
[53. g3 Re2+ 54. Rg2 Rxg2+ 55. Kxg2 Qe2+ 56. Kg1 Qf3 57. Kh2 Qf2+ 58. Kh1 Qxg3+ ]
53... Qf5 54. Qa2 h4
Collecting another advantage (weak gPawn, maybe a passed fPawn if White exchanges g for hPawn).
[54... Rc3 55. Qe2 Rc2]
55. Qd2?
Another donothing move, and this time it's fatal. The position is still interesting and may be no more than drawn, but I hope you can see the same attitudes at work here.
55... Qe4 56. Qf2 Rxh3# 01
A couple from Capa: the first is the game about which Euwe made his remark.
Capablanca,Jose  Vidmar,Milan sr [New York ] (12) [C98] 1927
1. e4 e5 2. Nf3 Nc6 3. Bb5 a6 4. Ba4 Nf6 5. OO Be7 6. Re1 b5 7. Bb3 d6 8. c3 Na5 9. Bc2 c5 10. d4 Qc7 11. Nbd2 OO 12. h3

12... Nc6 13. d5 Nd8 14. a4
A typical undermining thrust in the Ruy Lopez; Black's Pawns offer a target for White and counterplay for Black!
14... b4 15. Nc4 a5


"Whether this advantage is decisive or not does not interest Capablanca. He simply wins the ending! That's why he is Capablanca!"  EUWE
22. cxb4 cxb4 23. f3 Rfd8 24. Be3 h6 25. Red1 Bc6 26. Rac1 Be8 27. Kf2
KUFTE  "King Up For The Ending"!
27... Rxd1 28. Rxd1 Rc8

29. g4 Bd7 30. Bb6
Decisive. Now there are a couple of exchanges, which leave only White's best piece (Bb6) and Black's worst piece (Nf6) on the board! 30... Be6
[30... Ra8 31. Bc7 snookering the Rook [31. Rc1 and Rc5]]
31. Bxe6 fxe6 32. Rd8+ Rxd8 33. Bxd8 Nd7 34. Bxa5 Nc5

Capa seemed born with this facility at endgames.
Capablanca,Jose  Corzo y Principe,Juan (Havana m ) (09) [A83] 1901
1. d4This is the ninth game of the match for the Cuban Championship, which Capa played at the age of 12. He took 24 minutes over this game.
1... f5 2. e4 fxe4 3. Nc3 Nf6 4. Bg5 c6 5. Bxf6 exf6 6. Nxe4 d5 7. Ng3 Qe7+ 8. Qe2 Qxe2+ 9. Bxe2 Bd6 10. Nf3 OO 11. OO Bg4 12. h3
Black could try to play for a win with the two Bishops, but instead exchanges apparently seeking a draw.
12... Bxf3 13. Bxf3 Bxg3 14. fxg3 Nd7 15. Rfe1 Rae8 16. Kf1 f5 17. Rxe8 Rxe8 18. Re1 Rxe1+ 19. Kxe1 Nf6

[21... Nxg3 22. Kf4 Ne4
[22... Nf1 23. Be2 Nd2 24. Kxf5]
23. Kxf5]
22. Be2 Kf7 23. Kf4 Kf6
Chernev comments "The position may look drawish, but it is to Capablanca's liking; he often manages to squeeze a win out of a theoretical draw". I haven't seen a GM assessment of this position and Chernev (by no means a weak player) does not commit himself as to the 'proper' result of this endgame. Without wishing to enter the (possibly fruitless) debate about whether this position is in fact drawn, White does have the advantage of Bishop over Knight, with play on both sides of the board. If White can create tension in more than one area of the board, Black's Knight will find itself overcommitted. While all the Black Pawns are on the board and are all on light squares, White's Bishop lacks scope, but if things open up a little, the Black Pawns may become vulnerable.
24. h4 g6
[24... h6 25. h5]
25. g4 h6 26. g5+ hxg5+ 27. hxg5+ Ke7 28. g4 fxg4 29. Bd3

29... Nf5
concedes a passed Pawn
[29... Kf7 (Hooper) 30. Kxg4 Nb5 31. c3 Nc7 "with good drawing chances"; neither Bishop nor King have an obvious entry point.]
30. Kxg4 Nxd4
[30... Ke6 31. Bxf5+ gxf5+ 32. Kf4 and who has the most tempi to lose on the Queen'sside? Chernev assumes Black will run out of moves, but it's worth being sure! Perhaps..
32... a5
[32...b6 33. b4 a6
[33... a5 34. bxa5 bxa5 35. a4]
34. a4 a5 35. bxa5 bxa5 36. c3]
33. a4 b6 34. b3 b5 35. c3 b4 36. cxb4 axb4 37. a5]
31. Bxg6 c5 32. Kh5 Ne6 33. Kh6 Kf8 34. Bf5 Ng7
[34... Nd4 35. Bd7 Nxc2 36. g6 Kg8 37.
Be6+ Kh8 38. g7#]
35. Bc8 b6 36. g6 d4

37. b3 Kg8 38. a4 Kf8 39. Bg4 Ne8 40. Kh7 Ng7 41. Kh6 Ne8 42. Be2 Ng7 43. Bc4 Ne8

44. Kg5 Ke7
[44... Kg7 45. Bb5 Nd6 46. Bd3 Ne8 47. Kf5]
45. Kf5 Ng7+ 46. Ke5 Nh5
[46... Kd7 47. Kf6 Ne8+ 48. Kf7 Nd6+ 49. Kf8]
47. Be2 Ng7 48. Kd5 Ne8
[48... Kd7 49. Bg4+]
49. Kc6 Ng7 50. Kb7 Kd6

51. Kxa7 Kc7 52. Ka6 Ne8 53. Bf3 Ng7 54. Bd5 Ne8
[54... Nf5 55. Be4 Ng7 56. Kb5 Ne8 57. a5 Nd6+ 58. Ka6 Nxe4 59. axb6+ Kb8 60. g7 Nf6 61. Kb5 Kb7 62. Kxc5 Ng8 63. Kxd4]
55. Bf7 Ng7 56. Kb5
Now the White King covers the break at a5, and the Pawns at b6 and d5. 56... Nf5

[57... bxa5 58. Kxc5]
58. Ka6 bxa5
[58... Nf5 59. axb6+ Kb8 60. Kb5]
59. g7 10
Two last examples, which illustrate the same problem, although at rather different levels of the game...
MarshallCapablanca, 1909
1.d4 d5 2.c4 e6 3.Nc3 c5 4.cxd5 exd5 5.Nf3 Nc6 6.g3 Be6 7.Bg2 Be7 8.OO Nf6 9.Bg5 Ne4 10.Bxe7 Qxe7 11.Ne5 Nxd4 12.Nxe4 dxe4 13.e3 Nf3+ 14.Nxf3 exf3 15.Qxf3 OO 16.Rfc1

16...Rab8 17.Qe4 Qc7 18.Rc3 b5 19.a3 c4 20.Bf3 Rfd8 21.Rd1 Rxd1+ 22.Bxd1 Rd8 23.Bf3 g6 24.Qc6 Qe5 25.Qe4 Qxe4 26.Bxe4 Rd1+ {!} 27.Kg2 a5 28.Rc2 b4 29.axb4 axb4 30.Bf3 Rb1 31.Be2 b3 32.Rd2 Rc1 33.Bd1 c3 34.bxc3 b2 35.Rxb2 Rxd1 36.Rc2 Bf5 37.Rb2 Rc1 38.Rb3 Be4+ 39.Kh3 Rc2 40.f4 h5 41.g4 hxg4+ 42.Kxg4 Rxh2 43.Rb4 f5+ 44.Kg3 Re2 45.Rc4 Rxe3+ 46.Kh4 Kg7 47.Rc7+ Kf6 48.Rd7 Bg2 49.Rd6+ Kg7 01
There are some bones to pick in the details of this game, but the flow of it is very convincing. I believe that it is helpful to play over the whole of games like this quite quickly to start with, and then go back over the moves more slowly. Knowing what happens later can help you unpick the thread of the game to the point where a mistake was made, although here Capa points his finger firmly at the move of the King's Rook to defend the King'sside.
Democrito  DrDave: EICS rated blitz game EICS, Aarhus, Denmark (), 1997
1. e4 e5 2. Nf3 Nc6 3. Bb5 Bc5 4. Nc3 Nf6 5. d3 OO 6. OO d6 7. Bg5 h6 8. Bxf6 Qxf6 9. Nd5 Qd8 10. c3 a6 11. Ba4 b5 12. Bc2 Ne7 13. Ne3 f5 14. exf5 Nxf5 15. Nxf5 Bxf5 16. d4 Bxc2 17. Qxc2 exd4 18. Nxd4 Qf6 19. Rad1 Rae8 20. Rfe1 d5 21. Qd2 Bd6 22. Nf3 c6 23. Qd4 Qxd4 24. Nxd4 Rxe1+ 25. Rxe1 c5 26. Nf3 Kf7 27. Ne5+ Bxe5 28. Rxe5 Rd8

29. Kf1?! Kf6 30. Re2?
That Rook was fine where it was.
30...d4 31. cxd4 cxd4 32. f3?
Again, merely solid, not active.
32...d3 33. Rd2 Ke5 34. Ke1 Kd4 35. Kd1 Rd5 36. g3 Ke3 37. f4 g5 38. fxg5 hxg5 39. h4 Rf5 40. Ke1 gxh4 41. gxh4 Rf1+ 42. Kxf1 Kxd2 43. h5 Kc1 44. h6 d2 45. h7 d1=Q+ 46. Kf2 Qh5 White resigned 01