Qualifications
Sometimes, all you really need is some hands-on experience. Apply and get your hands dirty at a railroad company and you can probably just work your way up on the inside. Some train companies are going to want you to complete a six-week conductor training program that technical schools and community colleges offer.
Freight conductors will have a few extra qualifications, such as a valid driver's license and the ability to pass background and drug tests (source). You'll also learn about different types of cargo—including handling the dreaded hazardous materials that you may be unlucky enough to haul.
Besides training, you'll likely need to be certified as well (source). Trains and train tracks are a big part of infrastructure, so local, state, and the Federal government all have an interest in making sure you know what you're doing.