Most importantly that vowels in German are monolithic sounds, i.e. they don't change through the course of pronouncing them, nor do they change in different words (unless they are loanwords).
Example: The English "a" sound starts on "eh" and ends on "ee". The German "a" sound is just "uh" and always "uh." In other words, if you tell an English speaker to pronounce a very long "a" as you leave the room and send another person in and tell you what the person in the room pronounced, they will not know if he pronounced an "a", "e" or "i." You do the same in German and it will be perfectly clear they are saying "a."
Second most important rule is that the exception to this rule is the diphthong "eu"/"äu," which is pronounced like the "oy" in boy or toy.
Next is the pronunciation of the "ch." It changes depending on the vowels in front of it. For "a," "o," "u" and "au" it is the "hard ch," which sounds like you hocking up spit from the back of your throat. You do this by pushing you tongue up to the roof of your mouth while exhaling, making the soft pallet and uvula vibrate. For all other vowels it is the "soft ch," which sounds like a hissing cat. You do this by touching your lower front teeth with your tongue, while curving it upward, touching the sides of it to the roof of your mouth, making the air you exhale "whistle" past your upper front teeth.
Then there is the "z" sound, which is basically done by starting with your tongue in the position you would start a "t" with, but then going directly into an "s" and thereby creating an explosive transition into the "s."
There are of course many others, but theses are the once that most students need to work on the hardest.
HTH
