Press Alt with the appropriate letter. For example, to type ä, press Alt + A; to type ß, press Alt + S.
Stop the mouse over each button to learn its keyboard shortcut.
Shift + click a button to insert its upper-case form. Alt + click a button to copy a single character to the clipboard.
You can select text and press Ctrl + C to copy it to your document. In your target document, press Ctrl + V, or, if you want to paste the text without formatting, try Ctrl + Shift + V.