Hi! I've listened to your recording and I have some suggestions. I'm going to go sentence by sentence and give you advice for each of them.
1. Welcome to American accent training. This sounds really American, just make sure you clearly distinguishing between the t in accent and t in training. In the recording it sounds a bit like "accentraining." Your vowel sounds are spot on in this sentence though!
2.This book and CD is designed to get you started on american accent. This sentence was a little hard to understand around "book and CD is designed" I'm not sure I've heard exactly what you were trying to say.
When you say "this" make sure the s at the end is pronounced like the s in sister. (If you say "these" the s should be pronounced like a z.)
When you say "book" the oo should sound more like "ouh" The sound comes from the back of your mouth or throat, whereas the oo you use is more appropriate for "through"
3. We'll follow the book and go through thirteen lessons and all the exercises step by step. When you say thirteen, don't take so much time on the ir part of the word. You pronounce it like thiIIRRteen, but it will sound more American if you pronounce it like thurteen or thrrteen. We barely pronounce the i in thirteen.
With the word "lessons" don't put any stress on the syllables. Your "lessons" sounds like leehhhssons. It will sound more natural if you say it like "less in" It might help to say the word "listen" then change the i vowel to an e vowel to say "lesson" Listen and lesson are pronounced the same except for the first vowel in each.
For "step by step" just remember to use a s like the s in sister. This s is made by touching your tongue to the roof of your mouth just before your teeth and blowing are through, avoid using your throat to get a z sound in there.
4. Everything is explained in a complete answer key that may be found in the back of the text. One big thing that will make this sentence sound more natural is not making in abrupt sound changes (specificially when you say "explained in a complete")
"Everything" is pronounced in three steps (pronounced syllables): 1. Ev - make sure your top teeth are against your bottom lip and there is vibration when you say the v. 2. ry - sounds like the re in replaced, reheat, research, etc. 3. thing - make the th sound by putting your tongue flat against your top teeth, leaving space for air to flow through to produce the sound (you did this beautiful with "through" "thirteen", just work on applying the same sound in everything"
Text: make your e more ehhh sounding.... I'm not quite sure how to help you with this one!
I'm sorry this is so detailed but I hope it helps! If you want, send me the text of what you recorded and I'll send you a recording of myself saying the same thing.