Start with your DNR to get a feel for the laws. Every state is different.
What Jim said is a good place to start, first make sure you get things legally lined out, then once that is done if you are wondering what equipment to buy or tactics for various wildlife species there are tons of threads on this here in the archives. Many folks ask about "how do I startup" and folks will answer, but do check the search function on this website there are tons of folks who have offered lots of great info you can take and use to your benefit.
Obviously being legal is the first key, after this comes how will you advertise, what do you want to pursue (species wise), what insurance are you going to purchase to protect your customers in case of accidents, what equipment do you need, vehicle, overhead, etc....
If running it as a professional business there is much to do over the top of just finding a client to pay you. Depends on your goals, so folks might have a better idea how to answer if you throw a little more detail at us in terms of what you are looking to do, run a full time professional wildlife control outfit, or just part time make some extra money, or so forth...
Justin