Q:

How do you pronounce the ä in fällst or fällt?

My German book [1] says that ä is pronounced like the "ay" in "say". However, I have difficulty pronouncing it this way in words like fällt or fällst. Does the double consonant after ä shorten the vowel? Does it change its quality? How would you pronounce the words fällt and fällst? Would you pronounce fällt the same way we pronounce the English noun, "felt" (the textile)? This is the way which comes most naturally to me, but I suspect it might be a little off.
If there are regional differences in the pronunciation of these words, then I appreciate any explanation. Anything to help me say them with confidence. Thanks!
[1] The Everything Essential German Book by Edward Swick.

A:

I recommend pronouncing fällt like you would pronounce

Welt
bellt
stellt 
Held 
Feld
Zelt

and you will make no mistake. 
Or you make a sentence out of it:

Der Held gefällt, auch wenn er bellt, 
  bevor er in die Höhe schnellt. 
  Sein Zelt hat er aufs Feld gestellt. 
  Es ist die Welt, die ihm zu Füßen fällt. 

and pronounce everything the same way, just altering the initial consonant / consonant cluster / syllable.

A:

You can listen to the pronunciation of almost every German word here: https://de.forvo.com
If you search for fällt, you'll land on https://de.forvo.com/search/fällt/ where you can find 15 phrases, that all contain the German word fällt, spoken by different native speakers. Some of them are even spoken by more than one speaker, so that you even have more than 15 different audio files.
There are also some examples for fällst, but not as much as for fällt. 
The speakers are not professional speakers (i.e. they have no specific education in speaking like actors, radio announcers or something like that. They are just "normal people".)

If you want to listen to professional speakers, you need to visit http://www.adaba.at (adaba = Aussprachedatenbank = pronunciation database). Unfortunately this websites has an awful usability, so let me explain how it works:

Go to http://www.adaba.at 
In the 2nd window, titled »Suche« (which means search):  

click on »Orthographische Suche« (orthographic search)  
enter the word, that's pronunciation you want to know into the search field (for example: »fällt«)  
click on the magnifying glass (leave all other settings as they are, or use them to refine your search as you wish)

After a few seconds all words that contain your keyword will be listed above, in the 1st window, titled »Ergebnis« (result)
Select an item from this list (click it)
The phonetics will be shown in the country-list in the center of the Ergebnis-window. The flags mean:  

red, white, red: Austria
black, red, gold: Germany  
white cross on red background: Switzerland  

you can listen to a male and a female professional speaker for each country  

red: female  
blue: male

So, there are six speakers, and all of them are professional speakers, i.e. it's their profession to speak in the public. For example, the male Austrian speaker is Peter Fichna (he already died some years ago), who was for many years the chief speaker of the Austrian Broadcasting Corporation.

You can learn from both websites (the amateurs site and the professional site), that most of the German words are pronounced a little bit different in different regions. So don't care too much about the perfect pronunciation. As long, as you are close enough, you will be understood.
Also note: If you didn't learn German as a child, you always will keep an accent, depending on your native language. It is almost impossible for an adult learner to get rid of such a foreign accent. But that doesn't matter. People will know that you are not a native speaker as soon as you speak your first word, but nobody really cares. 
You will know lots of people with foreign accents too, like Arnold Schwarzenegger, who still has a really awful German accent, but in spite of this he became a famous actor and even a governor.

