Грамматика русского языка. Часть 1. Русский алфавит. Глава 5. Согласные Ж, Ц, Ч, Ш, Щ. Russian Grammar. Part 1. Russian Alphabet. Unit 5. The Consonants Ж, Ц, Ч, Ш, Щ.

The following Russian letters are quite easy to pronounce because there are similar sounds in English. However, in English, it is necessary to use several letters to represent these sounds; in Russian, each of these sounds has its own special letter. These letters are: ж [zheh], ц [tseh], ч [cheh], ш [shah], щ [shchah]. The letters sound harsher than in English. 

The letter Ж ж [transcribed zh]
The letter ж [zheh] sounds even harsher than in pleasure or vision.
Examples:
жук  [zhook] beetle
жажда  [zhahzh-duh] thirst
кожа [kaw-zhuh] skin

The letter Ц ц [transcribed ts]
The letter ц [tseh] sounds harsher than in quartz or cats.
Examples:
цукат  [tsoo-kaht] candied fruit
бац [bahts] bang
плац [plahts] parade ground

The letter Ч ч [transcribed ch]
The letter ч [cheh] sounds softer than the ch in church or child.
Examples:
почта [poch-tah] post office
час [chahs] hour
луч [looch] ray

The letter Ш ш [transcribed sh]
The letter ш [shah] sounds harsher than in nation.
Examples:
штат  [shtaht] state
шум  [shoom] noise
шанс [shahns] chance

The letter Щ щ [transcribed shch]
The letter щ [shchah] sounds similar to, but softer than the sound you hear in fresh chicken.
Examples:
плащ [plahshch] raincoat
щука [shchoo-kuh] pike (fish)
мощь [mawshch] power