Clark, the German keyboard is close enough to ours where I could still touch-type as long I remembered that the z and y keys are swapped. Except for that, I believe the letters and numbers are in the same place. The symbols are different and the umlaut characters are on the right side as well as the esset. For example, the ö is where the semicolon is on my keyboard and the ß is to the right of the zero.
Writing the letter "e" after a vowel that is normally umlautted is not originally an English innovation. Switzerland, which has 4 national languages, French, German, Italian, and Romansch, is where this tradition began. Many people in Western Switzerland had "French" typewriters which they had to use to type German letters. They had no umlauts, so they improvised by adding the e. They also got rid of "Ess-zett" by typing "ss", which has the same sound, and is being considered for adoption as part of regular German language convention today.
Yes, the German keyboard IS only a couple of letters different from the American and British keyboards, which is why all of you can adjust very easily. The good thing about the German keyboards is that they have keys specially for the accent and make good use of the ALT key for less important characters.
Here's the top row of the German keyboard:
° ! " § $ % & / ( ) = ? `
^ 1 2 3 4 5 6 7 8 9 0 ß ´
The ^ at the left is the accent circumflex. The ` and ´at the right are the accents grave and aigu. There are special keys for umlauted characters.