Ryan's answer is spot on-- forensic scientists that work for the government often don't make a boat load of money. However, like many jobs, there are several factors in play.
Most new forensic scientists that work for state governments don't make a lot of money, but your experience and position within your lab will have an impact on your salary. For example, a first year DNA analyst may make $50,000/ year, but an experienced DNA analyst who is also a CODIS administrator may make more than $80,000/year. Additionally, when you work for the government you will receive a pension after completing X years of service. Generally, at least 10 years is needed to be "vested" and receive money when you retire. Most private agencies don't offer anything like this.
Additionally, there are several private organizations such as BODE, ThermoFisher Scientifice, etc. who are private labs that do contracted work for forensic labs, other private labs, and do research. Getting hired in at a state forensic lab, gaining valuable experience (while getting vested in a pension) then transitioning to the private sector is a great way to earn more money, but most don't offer any sort of pension program.
Most importantly, it's critical to select a job that makes you happy! Forensic science careers are very fulfilling, but it's not a career path that makes millions of dollars.