When playing black I often find myself in a position where my knights are under attack early on in the game. (Such as 1. e4 e5 2. Nf3 Nc6 3. Bb5). It ends up being an even trade in material, but then my pawn structure is messed up. Any advice?

That’s the Ruy Lopez and there is nothing black can do about the knight under attack. (..a6) Is the normal response for black on move three preparing for (..b7) later on. Only advise is play a different open like Philidor’s Defense (1)e4,e5 (2)Nf3,d6.

In the specific position you give, I recommend recapturing with your d pawn rather than the more usual "towards the centre" rule, as this protects your e pawn indirectly.  1.e4 e5 2.Nf3 Nc6 3.Bb5 a6 4.Bxc6 is the exchange variation of the Ruy lopez.  My advice is not to fear it.  The alternative, 4.Ba4 is much more painful. 

In general, you will get the advantage of having 2 bishops, and you will get an open file for your rooks in exchange for your damaged pawn structure.  Also in general, giving up a bishop for a knight early is often not a good idea, because you become weaker on the colour of the bishop you lose, and your opponent will have lots of time to make plans to take advantage of this because things are rarely fixed early on.  For example, he could build up attacks on the weak colour squares, fix the pawns giving you a bad bishop, or he might decide to open up the position for his pair of bishops. 

Both very helpful posts. Thanks for the advice; I will use those suggestions in my future games.

Some things I have found useful to know when playing the black side of the Ruy Lopez:

• White playing 4. Bxc6 does not immediately expose the black pawn on e5 to attack from the white knight on f3, since 4...dxc6; 5. Nxe5 Qd4 forks the White's knight on e5 and pawn on e4: the knight will have to flee, allowing 6...Qxe4+, regaining the lost pawn.  Note that after 4...bxc6; 5. Nxe4 Black cannot play 5...Qd4 since he still has a pawn on d7, blocking the Queen.  
• Since the pawn on e5 is not immediately threatened after 3. Bb5, Black can play developing moves such as 3...Bc5 and 3...Nf6 (I prefer 3...Bc5 as it allows Black to play 4...d6 to, if necessary, support the pawn on e5 without interfering with the development of his kingside bishop).  If you play 3...Nf6, do not fall for 4. O-O Nxe4; 5. Re1, when Black's knight on e4 has to move (if it tries to stay on e4 with 5...f5, it will still have to move after 6. d3), allowing 6. Nxe5 when 6...Nxe5 is met by 7. Rxe5+.
• Black can also play 3...a6, when white will almost always use either 4. Bxc6 (which is met by 4...dxc6, of course) or 4. Ba4.  After 4. Bxc6 dxc6, Black has a terrible queenside pawn structure (doubled pawns, no pawns on the central d-file, and a pawn at a6 which is doing absolutely nothing on move 5 but which took up a turn to get to it's current position).  After 4. Bxc6 dxc6, White has the move and one more developed piece than Black, but has traded a bishop (a powerful weapon in a game without many pawns in the center to block it's diagonals) for a knight, a much less useful piece in an open game because it can't take advantage of the clear diagonals and files.  4. Ba4 is supposedly a better line than 4. Bxc6, but one which takes more study time to learn properly.  If white plays 4. Ba4, keep in mind that the tempting-looking 4...b5; 5. Bb3 leads to a weak queenside pawn structure, although it simplifies the game by removing the possibility of Bxc6 once and for all.
• In lines such as 1. e4 e5; 2. Nf3 Nc6; 3. Bb5 Bc5 and 1. e4 e5; 2. Nf3 Nc6; 3. Bb5 a6; 4. Ba4, if white can give his pawn on e4 adequate defenders, Bxc6 is threatened, since ...dxc6; Nxe5 Qd4; Nf3 and Black cannot take White's pawn on e4 with his queen since the pawn is already defended.  Example (I'm not advising that you play this, just presenting it to show when Bxc6 is dangerous to Black):  1. e4 e5; 2. Nf3 Nc6; 3. Bb5 Bc5; 4. d3 Nf6; 5. Bxc6 dxc6; 6. Nxe5 Qd4; 7. Nf3 and Black cannot play 7...Qxe4 (or 7...Nxe4, for that matter) because of 8. dxe4.  Notice that White's pawn on e4 is adequately defended in this case because, although Black has two pieces attacking e4, he still loses material after 7...Nxe4; 8. dxe4 Qxe4+ (he's traded a knight for two pawns).  However, White cannot play 5. Bxc6 after 1. e4 e5; 2. Nf3 Nc6; 3. Bb5 Bc5; 4. Nc3 Nf6 because after 5...dxc6; 6. Nxe4 Qd4; 7. Nf3, the pawn on e4 is not adequately defended:  7...Nxe4; 8. Nxe4 Qxe4+ and Black has traded a knight for a knight and a pawn.  This is because the defender of the e4 pawn was a knight, not a pawn as in the previous instance.  In cases where Bxc6 is a genuine threat, as in the first example, Black can resolve the issue by simply giving his pawn on e5 another defender, many times in the form of a pawn at d6. This ensures that the e5 pawn will still have a direct defender after the defending knight on c6 is traded for White's light-squared bishop.
• I always play 3...Bc5 against much lower rated players because some of them will play an immediate 4. Bxc6 even if I don't play 3...a6.  Against any other opponent, I will play either 3...a6 or 3...Bc5.

GuyOnTheCouch wrote:

Only advise is play a different open like Philidor’s Defense (1)e4,e5 (2)Nf3,d6.

Gawd. IMO the Philidor is a crippled defense. You allow very easy development for White with very little hope for counter play. I know there are exceptions. Stick with the Ruy Lopez and learn with it. If you want active, learn the exchange variations, the Schlieman, or the Marshal. A "C" encyclopedia wouldn't hurt either ;) Don't fret the loss of pawn structure. The minor exchange, loss of one of White's best pieces, and active lines are more than enough compensation. I'm an e4 player and I wouldn't dream of playing BxN in a serious game. My Bishop hunts Kings ;)

That's a good thing, Bishops are stronger than Knights.

I always play Nf6, the Berlin Defence. There's also a nice trap to play in this.