According to Swan (my grammar bible), common can equally be used with -er and -est as well as more and most.

Google says it's more common to say 'more common' (1,410,000)
instead of 'commoner' (89,200)
And it's most common to say 'most common' (3,150,000).
'Commonest' only has 101,000.
: )

wobei man noch bedenken muß, daß das Wort 'commoner' noch eine zweite Bedeutung hat - (einfacher) Bürger kann wohl so übersetzt werden

Comparatives and superlatives for words of three or more syllables invariably use more and most. Regular one syllable words always take -er, -est.

Two syllable words usually take -er / -est with some exceptions which, as near as I can tell, depends on how it sounds. "Naiver" and "tranquiler" both sound funny to me, but are listed as accepting both forms. But simpler, prettier, heavier and friendlier are fine.

Harmful, harmless, fragrant and poignant all must take more/most. Why? I don't know, it just sounds right to me.

Sorry I can't be more helpful (NOT helpfuler!) than that; maybe someone else can come up with the rule.

@Peter. The examples with pretty, friendly, etc. follow the rule that two-syllable adjectives ending with a "y" are formed in general with "ier" and "iest". Several others ending in an unstressed vowel (sorry to the non grammarians!) also end in "er" and "est" (e.g. narrow, simple, clever, quiet). Apart from that, a good single-language dictionary or grammar reference is needed!

Hab Euch mal schnell kopiert, was ich mal für eine meiner U-Stunden zusammengestellt habe. Ich hoffe, es schafft etwas Klarheit.

CComparative and Superlative adjectives
Essentially, there are two different ways to form the comparative or superlative.

1. Using -er, -est
1.1. all one-syllable adjectives
e.g. cold-colder-(the) coldest; young-younger-(the) youngest; poor-poorer-(the) poorest
1.2. one-syllable adjectives that end in one vowel + one consonant: these double the consonant and add -er, -est
e.g. big-bigger-(the) biggest; fat-fatter-(the) fattest
1.3. two-syllable adjectives ending in -y, -le, -er, -ow and two-syllable adjectives that are stressed on the second syllable
e.g. easy-easier-(the) easiest; happy-happier-(the) happiest; polite-politer-(the) politest
Note: Adjectives ending in -y change the y to i.
1.4. one-syllable adjectives ending in -e add -r, -st
e.g. late-later-(the)latest; fine-finer-(the) finest

2. Using more+ adjective, most+ adjective
2.1. Most of the two-syllable adjectives (cf. 1.3.)
e.g. polished-more polished-most polished; rapid-more rapid-most rapid
2.2. All polysyllabic adjectives (cf. 1.3., 2.1.)
e.g. difficult-more difficult-(the) most difficult; expensive-more expensive-(the) most expensive

Apart from these so called regular comparatives and superlatives there is a small group of irregular adjectives.
Here is a list of the most common irregular adjectives:

adjectivecomparativesuperlative
goodbetterbest
badworseworst
manymoremost
muchmore most
littlelessleast