Interning is difficult, although some departments allow it. The reason it is not encouraged is due to possible exposure of privileged and or sensitive case information. Additionally, there is a legal liability for any department that allows you to attend a crime scene. You may witness events and be called to tesitfy and or you may get injured.
If you are in school and working towards your degree in criminal justice, you ARE encouraged to apply for an internship. I am currently a 4th year student working on a B.S. in Criminal Justice and currently working as an intern in the local police department in investigations. You have to contact agencies to see if they have internships first of all. If they have internships, then you have to apply like if you were applying for a position. Try to contact the correct person who handles internships in that agency. If you are attending school, contact your career advisor and ask them how you go about getting an internship. If you are not in school, then I would think it would be hard to get an internship. You have to do the legwork and contact people. Good Luck!