Very crudely:
Phonetics is the study of the neurological bases of speech, the actions and movements of the vocal organs when we speak, the acoustics of the sound waves carrying speech and how speech is received by the ears and interpreted by the brain, I have underlined the part that is of most interest to language teachers.
Phonology is concerned with the sounds made in a particular language. The wallchart of symbols that some English teachers display in their rooms is usually a table of the English phonemes.
Prosody (or suprasegmental phonology) deall with such things as rhythm, stress, pitch and intonation.