One thing you'll need to do is become familiar with your local Health Department. You will need a permit from them to conduct your business.
In order to get a Board of Health permit in my area (and many others), you need to be Servesafe certified. Go to the Servesafe website for information on classes and testing in your area. There is also a lot of state by state Board of Health info on that site.
Dealing with the Board of Health really means dealing with the local Health Inspector-he or she is the person who you will deal with. Just like any other occupation, some are nice and some are jerks-I am lucky that my local Health Inspector is a fair and nice man-it doesn't hurt that he likes hot dogs too. Whether the person is nice or not, they are a resource. You can find the local Health Inspector's contact info on any municipalities' website. The best thing to do is call them up and politely engage them in a conversation. Tell them you want to open a hot dog stand, where you were thinking of locating (again if its on public land make sure you've checked out local restrictions and permits, if you're on private property let the inspector know where), let them know you'll be getting your Servesafe and ask them what you need to do. Most inspectors will be straightforward and let you know exactly what you need to do and what type of equipment will meet with local health codes.
Most Boards of Health are going to base their local regulations on NSF approved standards. Even so, different states and municipalities have their own regulations and rules, so it is best to find those out first. IMPORTANT NOTE: Most Boards of Health are going to require NSF approved sinks. That means FOUR SINKS: One each for washing, rinsing and sanitizing and a fourth for hand washing. Make sure you check with the local health inspector. Having NSF approved sinks and equipment will make every one's life easier!
For an alphabetical order list of links to state and local Boards of Health, click here or on the link in the Navigation area at the top of the right column. It pays to do your homework before talking to the local Health inspector. They're usually busy (or they want you to think they are) and an informed and concise conversation is better than asking a lot of dumb questions.
If you are looking at a specific cart, trailer or truck, make sure you have photos, drawings and a specification sheet when you meet with the inspector for the first time. If they have any concerns with your equipment, it is better to know about it and deal with it BEFORE they conduct an inspection.
Once you know what you need to pass the health inspection, you can go out and choose your cart, trailer or truck.