Pronunciation of the sounds «Ш» [Sh] and «Щ» [Shch] is a challenging task for most Russian language learners. However, this task is quite manageable. Practise in front of the mirror. Pay special attention to the position of your tongue and lips. The sounds eventually will become more clear.
The sound «Ш» [SH]
Move your tongue back and strain its root, lift the tip of your tongue to alveoli (teethridge), stretch your lips. The sound should resemble hissing. Like milk boils over or snake hisses. If the sound resembles whistle or you cannot produce it at all, do the following: stretch your lips, move the tip of your tongue to upper teeth and pronounce the sound «С» [S]. Pronounce it very slowly. Continuing pronunciation, move your tongue slowly to alveoli until you get the sound «Ш» [Sh]. When you get it, you will be able to pronounce it easily.
Do not afraid to experiment. Press the tip of your tongue closer to alveoli (you feel like the sound «stumbles» and stops), relax pressure and finally you will instinctively find the right position of speech apparatus to produce the sound «Ш» [Sh].
Phonetic exercises are the best to help in positioning of sounds. Even if you do not know meanings of some words but can read, it will be useful to repeat any words with the syllables «ША» [Sha], «ШО» [Sho] - «ШЁ» (read like [Sho]), «ШУ» [Shu] «ШИ» [Shi] «ШЕ» [She] on a regular basis.
Шапка [shapka], шахматы [shachmaty], шахтёр [shachtyor], шашка [shashka], шахта [shachta], шайба [shayba], шарф [sharf].
Шоколад [shikalat], шок [shok], шёпот [shopat], шёлк [sholk].
Шуба [shuba], шутник [shutnik], шутка [shutka], шум [shum].
Шерсть [sherst’], шесть [shest’], шелестит [shilestit].
Широко [shirako], шина [shina], шип [ship], шиповник [shipovnik].
The sound «Щ» [SHCH]
Positioning of the sound «Щ» [Shch] usually takes much more time than positioning of the sound «Ш» [Sh]. Sometimes it is also hard for foreigners to hear the difference between «Ш» and «Щ».
So let’s start again with articulation. Stretch your lips in smile (it would be easier), move the tip of your tongue closer to upper teeth, strain your tongue and move it to palate. Try to pronounce the sound «Щ» [Shch]. Remember, this sound would be longer then the sound «Ш» [Sh]. «Щ» is a soft sound. Keep your lips stretched.
If you get the sound resembling «Ф» [F], it means you rest the tip of your tongue against upper teeth. Lower the tip of your tongue, hide it behind upper teeth. Strain your tongue stronger.
If the sound resembles whistle or breath, stretch your lips in smile stronger. Strain your tongue. It should be the sense that the tongue is approaching to «stick» to palate but you do not allow it to do so.
If it resembles the sound «Х» [Kh], you’ve lowered your tongue too much and strained it. Weaken it lifting higher to palate. If you get the sound «Ш» [Sh], move your tongue forward closer to upper teeth.
As soon as you find the right sound, then the matter depends on practice.
Щётка [shchotka], щепка [shchepka], щетина [shchitina], щи [shchi], ищи [ishchi], полощи [palashchi], свищи [svishchi], щавель [shchavel’].