Yes there is a way without the need to install any additional software.
Step 1: In Ubuntu open the keyboard settings and enable Composite Key (System Settings -> Keyboard -> Shortcuts -> Typing -> Composite Key). When you click the value in front of Composite key (Disabled by default), you will get a list of keys to assign. Then choose one of them (Let us choose Right Alt for example). We will use this key for step 2.
Step 2: Know the key combinations
Ä is Right Alt + A + " (double quote) Ö is Right Alt + O + " (double quote) Ü is Right Alt + U + " (double quote) ä is Right Alt + a + " (double quote) ö is Right Alt + o + " (double quote) ü is Right Alt + u + " (double quote) ß is Right Alt + s + s € is Right Alt + c + = For example if you want to type the ü in Müller, first press Right Alt, then press u, then press " (double quotation mark).