1. You should contact the physician who administered the vaccine if you suspect your child has had a reaction to a vaccine. As documented in the book What Your Doctor May Not Tell You About Children's Vaccinations by Stephanie F. Cave MS, MD, physicians will not often report such problems which leads to under reporting of the statistics on vaccine adverse reactions and injury so don't stop at step one. There are limitations in the USA on compensation based on reporting timeframes so it is better to err on the side of caution.
    
2. If you live in Canada, reporting is primarily based on having your health care provider file a "voluntary" adverse reaction report; please make sure this is done. For more information on the process please see Guidelines for Reporting Adverse Events Associated with Vaccine Products. If you live in the United States of America then file a report with VAERS - Vaccine Adverse Events Reporting System.

If the reaction to the vaccine has left the child injured for life, or will need medical attention for the rest of their life, or even death, you will need to contact a lawyer who specializes in vaccine injury cases, for a list of lawyers or specialists go to  Vaccine Injury Lawyers and find one in your area. The lawyer will have to file a claim with the U.S. Court of Federal Claims. The claim goes through the NVICP (National Vaccine Injury Compensation Program). This process, if using the right lawyer, should only take 2 to 3 years to go through. People who did not have the right representation have been in the system for as long as 8 years. So do yourself a favor and get the right lawyer the first time. Please understand this: At no time should any of the lawyers who specialize in vaccine injury cases ask for any money up front. They may ask you to pay for any expert services, that is normal. But you should not pay for their fees what so ever. The government will compensate them for their time and fees regardless if your claim wins or looses.