1. Check accreditation. While a number of online high schools will claim accreditation, it is not the type that will be accepted by colleges and employers. An online high school should be accredited by DETC, CITA, AALE, or one of the six regional accreditors (that can be found at CHEA.org).
2. History. How long has the school been in existence? While new schools are formed all the time, having a longer tradition of offering courses, typically makes for better schools. Some of these schools have been open for decades as pre-Internet correspondence schools. This can be an advantage in producing quality programs.
3. Standard references. Is the school listed in one of the standard references like Complete Guide to Online High Schools: Distance Learning Options for Teens & Adults (Degree Press, 2007) or Bears' Guide to Earning High School Diplomas Nontraditionally (Ten Speed Press, 2003). Being listed is not necessarily a hallmark of legitimacy, but it helps.
4. Cost. Some of these online high schools are free public charter schools while others are quite expensive private high schools. The most expensive that I have come across is attached to a university in the south. Is there an advantage to paying more? Not really, but there may be an advantage with your program being attached to a university. However, being attached to a university most definitely does not mean that it must cost more.
5. Independent study or teacher-led. There are two basic types of programs. The first gives you the materials and you work through them on your own. The second provides you with a teacher, either one-to-one or similar to a classroom, and instruction is given. Neither is necessarily better than the other, but you should decide what sort of learning experience you need or want. There is a third option, more of a hybrid solution, and that is programs, like Laurel Springs School, that provides you with the amount of support that you, personally, need.
While this is only the beginning, it is a good place to start. You can also check out BestOnlineHighSchools.com for listings of schools.