recently I have taken to boiling it down like this when someone asks me where to start:
1) Make a list of the childhood vaccines
Useful resources for this step: Your country's recommended vaccine schedule (perhaps glance at other countries as well, get an idea of what is out there)
2) learn about the disease that these vaccines are meant to protect against
Useful resources for this step: CDC Pink Book, threads at mothering.com (for example, the archives on DTaP has a lot of good info on pertussis)
3) Decide which, if any, you find you want to learn more about the vaccine for (if, say, you don't think chicken pox is an issue, then you can probably skip the other steps)
4) Educate yourself on that specific vaccine:
-is it successful?
-does it prevent transmission?
-does it have any worrisome ingredients? do ingredients differ with brand?
-what are the side effects?
Useful resources for this step: Dr Sears Vaccine Book (or other works talked about here a lot), Insidevaccines.com, 909shot, immunize.org, VAERS database, the package inserts for the vaccines, the clinical trials of the vaccines:
http://www.clinicalstudyresults.org/ ,
http://www.clinicaltrials.gov/
5) Do your own risk benefit analysis- weigh the pros and cons of getting the vaccine and not getting the vaccine-- or however you see the question to be. You can even write it out on a sheet of paper in a few columns.