A site that I have used for transcription is for
CastingWords through Mechanical Turk. It's great practice, and they pay, too...just not very much. Of course, I didn't do it for the pay, but the practice. They are 100% legit and I've been transcribing for them for years now. Any money you earn can go toward an Amazon gift certificate account or transferred to your bank through Amazon Payments.
If you work for them, be VERY sure to read through their style guide and get it right the first time. Others will grade you according to that guide and it will have an impact on how much you earn, if you care about that. But if you're wanting to improve your transcription skills, then I assume you care.
Additionally, I HIGHLY suggest the use of
Express Scribe software. It's free software and I use it constantly. Some people use the foot pedal, but I just use the keyboard shortcuts. And of course, a really high quality headset is essential for accurate transcription. It can make all the difference when you are trying to decipher words.
(PS--This is my first post here so I hope I'm not breaking any terms by mentioning those sites and software. I consider them to be tools of the trade and find them very valuable, especially the free software part.)