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.
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.