Aviator FK -
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The best dispatcher training (with outstanding reputation with airlines) is Sheffield School of Aeronautics. They are known by US airlines and foreign air carriers as well. They are located in Ft. Lauderdale, FL, and their training takes some 8 weeks. The cost in approximately $5,000, all inclusive. Several sessions are available each calendar year. See their website.
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Flight Safety offers dispatcher training too, but they are more bizjet oriented for flight department of corporate operators and are apparently slightly more expensive than Sheffield.
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Of course you can study the written FAA Flight Dispatcher test, by using the FAA ATP study books, study FAR 25, 65, 91 and 121, and pass the written (valid two years) but still will need to pass an FAA flight dispatcher oral and practical test, and meet some practical training requirements with an airline using a dispatch or flight following system, such as a FAR 121 air carrier, to finally get the certificate.
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A pilot who takes a written FAA ATP and passes with a score of 90%, can probably pass the flight dispatcher written with 80% or more, if he knows some of the specifics of FAR 65. The theory is about same, meteorology, flight planning, performance, regulations, navigation, weight and balance, and publications, etc.
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While big airlines do their own dispatcher training internally, such as United or American, the smaller carriers could hire you to work in their flight operations department as assistant at "minimum wages", and tell you to get training for a certificate at i.e. Sheffield. I knew the son of a friend who did it in this manner with Atlas in Long Beach, CA.
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Good luck to you.
Happy contrails