Read and study books on specific languages and their origins, history and dialects. You can learn a lot about dialects by studying how various languages began and evolved over time, as well as how they differ by region or economic or social class.
Enroll in voice-training classes at a university, community college or private acting school. You'll learn to project and modulate your voice, as well as enunciate clearly. Some college theater departmetns offer beginning and advanced dialect classes, which you should enroll in, as well. Also look for a dialect coach in your area who might be willing to take on an apprentice or intern in exchange for your assistance with administrative or classroom needs.
Purchase dialect-training CDs, which are widely available for sale on the Internet and in some bookstores. Study American, British, French, Italian, German, Russian, Spanish, Chinese and Indian accents first, as these are some of the most widely spoken dialects. Many languages, such as English, Spanish and Chinese, have numerous dialects, which you'll also need to practice.
Watch films in which your chosen dialects are spoken and study inflections and tone. After each character speaks, pause your DVD player or VCR and repeat what you've heard. Practice as much as you can, whenever you can.
Create a reel that highlights your best dialects and voices; then apply for jobs with acting schools. Also contact film production companies and stage theaters, which might need dialect coaches for specific productions.
Create a website where people can listen to your reel and learn more about your services. Include a section of testimonials or recommendations from clients with whom you've worked in the past. Advertise on websites related to acting, film and theater, and also post ads on online classified sites such as Craigslist. Often, word-of-mouth is the best advertising, so spread the word throughout your local film, theater and television acting community.