Comparisons
Comparatives usually add -er and use als for “than”. Some add an umlaut: alt → älter. Predicate superlatives use am … -sten. Irregular: gut → besser → am besten; viel → mehr → am meisten.
Understand the idea
A comparative compares two things; a superlative selects the highest degree within a group. German often adds -er for the comparative and uses am … -sten for a predicate or adverbial superlative. Some forms change vowels or are irregular.
Build it step by step
Use als after a comparative when expressing than. Equality normally uses so … wie. Short adjectives may add an umlaut in the comparative. Learn gut → besser → am besten as a complete irregular set. Before a noun, a superlative also takes the required adjective ending, instead of simply keeping the am-form.
See it in a sentence
Mein Bruder ist älter als ich.
Deutsch gefällt mir besser als Mathe.
A useful memory aid
Practise three forms as one unit, not three unrelated words: groß, größer, am größten. Attach a comparison phrase to a real object or person.
A common trap
Do not use wie as a standard substitute for als after a comparative. Also avoid regularising gut as guter when you mean better.