Phonetics includes everything that is related to the physical realisation of the sounds of speech. Intonation characterises in particular the rhythm and pitch levels of a language and is also a part of phonetics.
It is in this area that I usually begin with my pronunciation training, for intonation is what constitutes the "typical sound" of a language. As babies we learn this side of language first. A baby's body mimics the speech rhythm and its voice imitates the pitch. Consequently it is often very difficult to emulate "foreign" speech intonation because the intonation of our own language is anchored deep within our personalities.
When the intonation "flows", the practice of uttering sounds individually is rendered in some measure unnecessary because the rules of rhythm carry part of the speech. The German language has a very marked speech rhythm with constantly varying emphasis, length of syllables and pauses, something that many other languages do not have in the same way. In addition, we signal the most important syllable with a change in pitch (highest or lowest position). From this result fixed speech patterns which are by no means solely dependent on the situation or the individual, even though there is a large scope for flexibility.
In my teaching I also work with breathing, articulation and the pronunciation of individual sounds.