A direct quote from the NRA/IRA Guide to Interstate Transportation states:
Federal law does not restrict individuals (except convicted felons; persons under indictment for felonies; adjudicated “mental defectives” or those who have been involuntarily committed to mental institutions; illegal drug users; illegal aliens and most nonimmigrant aliens; dishonorably discharged veterans; those who have renounced their U.S. citizenship; fugitives from justice; persons convicted of misdemeanor crimes of domestic violence; and persons subject to domestic violence restraining orders) from transporting legally acquired firearms across state lines for lawful purposes. Therefore, no federal permit is required (or available) for the interstate transportation of firearms.
Each state has its own laws regarding the right to carry. Gary Slider of handgunlaw.us has an extremely informative and up to date website, with interactive maps and links to applications for permits in each state. This site is frequently updated and has a simple format. Gary answers every e-mail personally.
There is no uniform state transportation procedure for firearms. If in doubt, a traveler should carry firearms unloaded, locked in a case, and stored in an area (such as a trunk or attached toolbox) where they are inaccessible from a vehicle’s passenger compartment and not visible from outside the vehicle. Any ammunition should be stored in a separate locked container.
Authorities may search anywhere within your reach without a search warrant after a valid stop. They may not open and search closed luggage without probable cause to believe evidence of a crime will be found. This applies particularly to luggage in locked storage areas or the trunk of a vehicle. Consent is necessary for such search. You have the right not to consent.
You also have the right to remain silent.
A provision of the federal law known as the Firearms Owners Protection Act, or FOPA, protects those who are transporting firearms for lawful purposes from local restrictions which would otherwise prohibit passage. A provision under FOPA was that persons traveling from one place to another cannot be incarcerated for a firearms offense in a state that has strict gun control laws if the traveler is just passing through (short stops for food and gas), provided that the firearms and ammunition are not immediately accessible, that the firearms are unloaded and, in the case of a vehicle, locked in a separate storage area.
New York, New Jersey, Massachusetts, Maryland and Illinois seem to be cited in various articles as “problem areas” for concealed carry law. It’s also been mentioned that the laws vary when you’re on American Indian reservations. There are about 800 Native American tribes listed by the federal government. Handgunlaw.us has a comprehensive breakdown of the ones with information available online.
Note: This article is not to be considered as legal advice or a restatement of law. To determine the applicability of these laws to specific situations which you may encounter, you are strongly urged to consult a local attorney.