Good points by PP
When we moved to NC we used ncreportcard.com or something like that. I imagine many states have similar info published. The schools our children are attending send us this info every year as well once the grading is done. Here, there were some statewide changes in the standardized tests that affected some of the scoring so keep stuff like that in mind when reviewing school district info.
Some things we did when deciding where to live (a.k.a. which schools we wanted our children to attend - not just which district, but which schools within our district)...
We researched online the info I noted above. From these school "report cards" we looked at: the average class sizes for each grade; the total student body population; standardized test results; attendance percentages; technology available in the schools; safety info; number & percentage of accredited teachers; gifted (or exceptional depending on your needs) education; honors/AP courses available; percentage of students going to college. In NC, the info that is included on the report cards for an individual school compare many of these things to the district and the state averages as well.
Once we narrowed down to which district, we drove to the schools to see what they looked like. What kind of neighborhood are they in? How old are the buildings? We also looked at the district websites. You also should keep in mind whether districts go year-round or under a traditional calendar (and whether all schools in a district are the same - I know someone whose district had elementary year-round but HS was traditional, and had kids on different schedules).
For us, we had a general vicinity of where to look due to DH's job. It did not take very long to narrow down to where we'd like to move.
Don't let it overwhelm you. Once you start comparing you'll find a good fit.
p.s. if you are using a realtor to find a house, they can give you feedback as well. Driving around different neighborhoods near schools you could also ask parents you see. Or visit the schools.