Also I should point out that the geometric intuition provided by Andreas Floer in some of his early papers is really quite beautiful and illuminating. For example read the introduction to his 1989 paper, Symplectic Fixed Points and Holomorphic Spheres, in Comm. Math. Phys (120) 575-611.
For the grittier details it's better to look in something like Dietmar's notes or the big book of J-holomorphic curves.