In the United States, many technical writing courses and degree programs exist for hopeful writers. Technical writers in other countries are not necessarily so fortunate.
I don't know why this should be so, but I am happy to say that this situation is improving; more and more universities and colleges are offering technical writing degrees and certificates. Since the number of schools offering technical writing programs changes frequently, providing a list of them here would soon cause this page to become out of date.
To find out what technical writing courses are available in your area, contact your local universities and colleges. If there are no classes offered in your area, some universities and colleges provide online degree programs that you can complete from anywhere in the world. Also, many private companies provide technical writing courses. You can find these by typing "technical writing courses" at the search engines.
Even if your local university or college does not offer any technical writing courses, you can take other courses that will be beneficial when you apply for a job:
Take an advanced course that will teach you how to use Microsoft Word. Many, if not most, adult education programs offer courses on how to use this software.
Better still, take a FrameMaker course if one is available.
Take a course in English Literature. This will teach you how to read and write critically.
Take a Logic course. Logic is most likely offered at the university level by the Philosophy department. As a technical writer, the questions you will most frequently ask yourself as you write your documentation are "Does this make sense?" and "Is this logical?" Learn how to think like Spock!
Take a programming course, specifically, one that describes object-oriented programming.
Do read all the pages in this site! Unlike a school-based technical writing course, docsymmetry.com is free and does not give you any assignments. It does, however, provide many suggestions on how to write excellent documentation. In particular, Becoming a Technical Writer and Hiring a Technical Writer provide you with very concrete information. If you study these and the other articles on this site carefully, and if you create a sample book (let the sample book be your assignment!), you should become quite a knowledgeable technical writer.
Finally, join the STC. Most STC chapters regularly host lectures and workshops that will not only aid you in your technical writing career, but will also provide you with many networking opportunities.