Assuming that you've never played Amateur Surgeon, and there is no real need to have played it to catch on to the story in the sequel, you can walk in knowing that Amateur Surgeon 2 will be one of the most natural, funny, and polished games that you will play with in the App Store. Like many apps in the App Store, it is a port of a Flash classic, but this one actually feels more natural with the touch interface than with the standard mouse.
The games story takes place 50 years after the events of the original, with you once again taking control of Allen Probe. Unlike the plot in the original though, Allen is in dire straights, his hospitals were shut down by the president, his family left, and his skills are rusty. While the situation may be different, once the surgeries start, the game is much more fun than the original. The surgeries are all fun and extremely interactive, forcing you to use combinations of pizza cutters, lighters, chainsaws, stitches, and more to fix your patients' unique problems, including some massive "cosmetic" implants and involve bug/animal extractions. None of the patients seem like fillers, all of them have humorous personalities and stories that move the game along nicely.
For the small amount of money that you will spend purchasing the game, there is really no better game out there in the App Store. Amateur Surgeon 2 certainly isn't the longest game that you will run into in the App Store, but its gameplay experience is like a sweet morsel of wonderful app goodness. If you appreciate something a bit off the wall, you will certainly love Amateur Surgeon 2.