Don't use the API system-waste of money for Salmonella. The comment from M. Musgrove is by and large accurate, apart from the fact that reptiles are cold-blooded and may carry both serovars of S. enterica and also Salmonella bongori. As such culture is still arguably the better method. Selenite enrichment followed by a selective media- Brilliant Green, XLD, RV or one of the newer commercial agar should work relatively well. If you wish PCR is a reasonable confirmatory test for S. enterica with genes such as invA and the aforementioned hilA found in visually all isolates. If you want to type the isolates then MLST should also tell you the serotype and is cheaper unless you already have the full set of typing sera.
If you want just to detect Salmonella maybe the easiest way is to do PCR or QPCR, after overnight incubation of cloacal swabs in the buffered peptone water. There are many protocols for detection of invA or other genes as already mentioned above by Dr Wigley.
If you want to isolate Salmonella then I suggest the method we used to isolate it from snakes and turtles. It is practically the same method that we use to isolate Salmonella from poultry feces, ISO 6579:2002 Annex D. It uses modified semisolid Rappaport Vassiliadis medium which is, in our experience, more sensitive and selective then method with RV and MKTTn, which was mentioned above by dr Musgrove. When you isolate Salmonella then you can serotype it, or do some other typing depending on your needs. API will not help you within species sub typing.