After studying some foundation of Gromow-Witten invariants, I now would like to see an explicit computation. I heard that one should first take a look at the total space of $\mathcal{O}(-1)^{\oplus2}$ over $\mathbb{P}^1$ or the total space of the canonical bundle of Fano surface (local Calabi-Yau). They can be worked out very explicitly via equivariant cohomology and localization. (Or there may be more tractable examples)

Could someone kindly suggest a paper or lecture note where I can start learning these examples and technique? Any suggestion is welcome.