There are three ways to compare things in German:
When they are equal: (No marker on adjective)
Er ist so groß wie ich. He is as tall as I (am).
Sie läuft so schnell wie er. She runs as fast as he (does).
(Note: the noun following "wie" is nominative)
When they are not equal: (Marker "-er" on adjective, as in English)
Comparative forms get umlauts if the adjective is one-syllable
Mein VW fährt schneller als dein Mercedes. My VW goes faster than your Mercedes.
(Note: the noun following "als" is nominative case!)
When one is the "most" something (Marker "-st + ending" on adjective)
Note: Superlative forms get umlauts if the adjective is one-syllable:):
Meine Mutter ist am schönsten. My mother is most beautiful.
Dein VW fährt am schnellsten. Your VW goes fastest.
NOTE: the "am + ___ -sten" form only works as an adverb or in cases where the normal form of the adjective would have NO ENDING:
The endings -ER and -(E)ST are NOT adjective endings, they are MARKERS for comparative forms. Adjectives with these markers may ALSO have adjective endings if they are followed by a noun (-st always has an ending):
As with regular adjective, superlative
and comparative adjectives take ADJECTIVE
ENDINGS if they occur in front of the noun that they modify:
fahre mit dem schnelleren Auto. I drive
with the faster car.