Well, the best place is to enroll in a Biology/Zoology program at a good University and tailor your studies in that direction. There you will have all the guidance, reference, equipment, etc. that you need to research whatever you are interested in within that discipline, and the vehicles to publish your findings. It helps to have a solid background in Biology. There you will learn the approaches techniques for scientific research, discovery, analysis of collected data, documentation, etc.
Or, you can fund your own research (or apply for grants) in whatever area interests you, join an organization such as SSAR and submit your studies and findings to them. If they are up to snuff, they may be published in Herpetological Journal, or whatever the publication is for the society you join.
As far as areas to research, there are as many of those as there are herps. You just have to decide what area interests you and go for it. But there are really no shortcuts. It doesn't matter what you find with your research, if you can't publish it in the proper format and articulate it in the proper language, it's not going to get any attention. Conducting research and compiling and analyzing the data and then making sure that your findings are sound scientifically and of some interest is no cake walk. Some possible areas are in Field Herpetology studying natural range of occurrence, habits of herps in the wild (feeding, mating, movement, etc.), predation, diseases in wild populations, Impact studies (effects of habitat loss), population surveys. Or laboratory herpetology, (LD50 studies, captive propagation studies, DNA studies for reclassification and verification of current taxonomy, pathology in captive reptiles, etc.) I could go on and on and on, but you get the idea and you see from this that some of the fields of study would require fairly sophisticated equipment and skills. If you think, for instance that a new species of Coccidia is causing problems in reptiles, it's tough to spring from your checkbook and buy and electron scanning microscope and DNA sequencing equipment to verify that what you've found is, in fact, a new species.
On the other hand, perfectly valid research can be accomplished just by keeping very accurate and extensive records of everything you do while going about the business of maintaining and breeding your own collection of captive reptiles. Some of the most important husbandry and breeding techniques were developed by hobbyists and private breeders who kept good records and tried different things.
Another good place to get a chance to participate in research is working at a zoo. A great deal of research in herpetology is conducted by zoos.