Qualifications
As you can probably tell, speech therapy is a pretty important job, and the powers that be don't want you messing it up. Because of this, SLPs are expected to complete both undergrad and graduate degrees, and get certified with the American Speech-Language Hearing Association (ASHA.) Somewhere in between grad school and the certification test, SLPs enroll in a 36 week clinical fellowship, where a mentor helps them practice the job with training wheels on. This is sometimes called a “clinical fellowship year,” or CFY, though it can take longer than a year to complete. You can work part time at your fellowship, or you can try to cram in more than the recommended 35 hours a week, but there's no cheating that 36 week minimum. But don’t panic—beyond the clinical fellowship lies your new life as a for-realsies speech-language pathologist! And did we mention you get paid for your training labors?
Depending on where you want to go from there, there might be a few more steps, such as meeting individual state requirements, ongoing credential upkeep with ASHA, and going for a PhD, if you want to teach or do research. But that's just frosting on the cake. Basically, do whatever ASHA tells you to do, and you can't go wrong.