Learn to really use your voice in the proper manner. According to Ray Mardo, a DJ trainer, you'll have to work on inflection, articulation and projection. You have to figure out how to pronounce words for best effect and be able to modulate the pitch and volume of your voice to your best advantage. Most importantly, people have to know what you are saying.
Understand the basic rules the FCC requires DJs to follow. While the FCC no longer requires DJs to have operating licenses to run a station, there are plenty of other regulations. For example, radio stations must announce their frequency and broadcast location around the top of the hour. Florida A&M emphasizes this "legal ID" requirement to their students.
Attend a school of broadcasting if you have the time (and money) to give you real-world experience in addition to the lectures you'll hear from real radio professionals. For example, the program at the University of Massachusetts, Amherst, gives interested students a chance to host a show on WMUA, the student station.
Make an aircheck that demonstrates your skills on the microphone. An aircheck is an example of what a DJ says between songs or when they do the station ID. You can make a basic aircheck with a cheap microphone and the sound recorder on your computer, or you can invest more money and go into a studio. Joe's Radio Air Check Page (see Resources section) gives you lots of examples.
Send your aircheck out to the stations in your area that interest you. Include a letter of introduction that reinforces why they should hire you as a DJ on their station. These jobs are extremely competitive, but if you are lucky, you may be offered an internship or an overnight broadcast slot.
Start out at community radio. If you cannot secure a professional DJ gig, there are community radio stations that allow public access for just about anyone who wants to do a show. Central Oregon's KPOV has some prerequisites, including a DJ course, but it offers real-world DJ experience to those in the area.
Broadcast your own show over the Web. With the recent advent of Internet radio, anyone with a computer and microphone can create their own show and send it out to the rest of the world. You may not ever be paid for Internet radio, but you will still be able to call yourself a disc jockey.