Some examples:"ei" like in "Eimer"(what means bucket) is spoken like the "I" in English.
"ä" like in "Ärger"(what means trouble) is spoken like the "a" in "wake up" in English.
"ö" like in "Ökonomie" (what means economy) is spoken like the "o" in "word" in English.
"ü" like in "Dünger" (what means dung) is spoken like the "y" in "lyrics" in English.
"ie" like in "Wien" (what means Vienna) is spoken like the long "e" in "meme" in English, not like the short "i" in "mixture".
But seriously: Buy a book.