Short adverbs having just one syllable form the comparative and the superlative by the addition of –er and –est to the positive.

Hard (positive), harder (comparative), hardest (superlative)
Soon, sooner, soonest
Fast, faster, fastest
Late, later, latest
Loud, louder, loudest
Clean, cleaner, cleanest
Clear, clearer, clearest
Low, lower, lowest
High, higher, highest

Note that almost all adverbs which are also used as adjectives belong to this class.

Adverbs ending in –ly

Adverbs which end in –ly take more for the comparative and most for the superlative.

Softly (positive), more softly (comparative), most softly (superlative)
Happily, more happily, most happily
Swiftly, more swiftly, most swiftly
Ably, more ably, most ably
Truly, more truly, most truly
Greedily, more greedily, most greedily
Efficiently, more efficiently, most efficiently
Certainly, more certainly, most certainly
Painfully, more painfully, most painfully
Joyfully, more joyfully, most joyfully

Exception

The adverb early is an exception to this rule.

Early (positive), earlier (comparative), earliest (superlative)

Some adverbs form their comparative and superlative degrees in an irregular manner:

Far (positive), farther, further (comparative), farthest, furthest (superlative)
Late (positive), later (comparative), last, latest (superlative)
Well (positive), better (comparative), best (superlative)
Badly, worse, worst
Little, less, least
Much, more, most

Notes

It should be noted that only adverbs of time, degree and manner have three degrees of comparison.

Adverbs such as now, then, once, there, where, why, how, not, never, ever etc., cannot be compared and hence they do not have the three degrees of comparison.