What is the difference between the pronunciation of Ш and Щ ?

Question

Answer

Let's play with words! 
Listen and repeat:

ШАПКА  --- ЩЕПКА

ШУТКА  --- ЩЁТКА

ШУБА  --- ЩУКА

I did for you an audio file. :) Here you can download the audio file.
http://rapidshare.com/files/171996113/10dec_1136.mp3.html

Answer

I am not competent in the question, but I'm native speaker :)
So, lets try to make these sounds. First of all, I hope you know english sounds CH and SH.
Russian Ш is almost the same as english SH.
There are no sound as Щ in English. But you can stretch out english СH ( Ch-h-h-h-h... )
So, beginning of this stretched sound will sound like standard CH, but the ending will sound like russian Щ.
Note the position of you tongue while making these sounds. In case of SH your tongue is above, but in case of CH your tongue is at the bottom. Then repeat sound SH but hold your tongue in position of CH and then practice, practice and more and more and more...
I think the position of the tongue is the main difference of these sounds.
I think so, but I am not sure.

With best regards, Sasha.

Answer

Щ seems to influence the next vowel sound.
for example:

Щавель would sound the same as - ШЯвель
Шип is pronounced with Ы Шып whereas Щип sounds with clear И
Щель - clear Е sound, but if there were a word Шель, then it would sound like ШЭль

Before equal sign (=) - how the word is written; After - how the word is pronounced
 Ша = Ша; Ща = Шя
Ше = Шэ; Ще = Ше
Шу = Шу; Щу = Шю
Шо = Шо; Що - Шё
Шё (шёлк) - Шо; Щё (щёки) - Шё
Шю \ Щю - не бывает
Шэ \ Шэ  - не бывает
Шы \ Шы - пиши через И (не бывает)
Шя \ Щя - не бывает

There are no words with the consonant sound after Щ.

Answer

'Щ' approximately sounds like 'sh' in "sheep" (softer).
'Ш' sounds like 'sh'  in "ship" or "shine" or "russian" but more hard, I guess.

Answer

same like first sound in the word  "sure"