If you are familiar with the concept of hard and soft consonants (or palatalized and non-palatalized), Ш is a hard consonant, and Щ is soft.
Ш sounds harder than the English "sh", and you need to put the tip of your tongue slightly further back than for "sh". Try searching forvo.com for such words as шапка, шуба, шнур.
Щ, on the other hand is softer than "sh", but more intense, and you need to move the tip of your tongue more forward. Search forvo.com for щука, щель, щипцы.
Also try listening to the following pairs side by side:
шапка - счастье ("сч" gives the same sound as "щ")
шерсть - щель
ширма - щит
шорох - щёлочь
шум - щуплый