As German does not distinguish between adjectives and adverbs in predicative position , what is said here with regard to adjectives applies equally to adverbs. The comparative form of the adjective, i.e. when stating that something is ‘bigger’ or ‘smaller’ etc. than something else, is formed in German as in English, i.e. by the addition of -er to the adjective, e.g
klein  => kleiner 
small => smaller
billig  => billiger 
cheap => cheaper

When adding the -er ending, the vowel of the adjective is usually umlauted, if it can be, i.e. if it is an a, o or u, e.g.

warm  => wärmer 
warm  =>  warmer
groß  => größer 
big  => bigger
klug  => klüger 
clever  => cleverer

Adjectives containing au never umlaut, e.g.

grau  => grauer 
grey  => greyer
schlau => schlauer 
smart  => smarter

There is a substantial number of additional adjectives that do not umlaut  despite containing an umlautable vowel, e.g

brav, bunt, dunkel, falsch, l ach, froh, hohl, kahl, klar, knapp,  lahm, morsch, nackt, platt, plump, rasch, roh, rund, sanft, satt,  schlank, stolz, stumm, stumpf, toll, voll, wahr, zahm.

In the case of the following adjectives usage varies: bang, blass, glatt, dumm, fromm, gesund, krumm, nass, schmal, zar. There are just a few adjectives/adverbs that have an irregular comparative, e.g.

gern =>  lieber 
like =>  prefer 
gut => besser 
good => better 
hoch => höher 
high => higher 
nah => näher 
viel => mehr 
much => more

Note the following. When an English adjective/adverb contains more than two syllables, and sometimes even if it has only two syllables, we prefer to form its comparative by means of ‘more’ rather than adding -er; however long the word is in German, add -er to the end of it, e.g.

interessant => interessanter
interesting => more interesting
oft => öfter
often => more often/oftene

Adjectives that end in -e simply add -r, e.g müde => müder
tired => more tired

Adjectives that end in unstressed -el and -er drop that e when adding the -er ending, e.g.
dunkel => dunkler
dark => darker
teuer => teurer
expensive => more expensive