Latin teachers typically use the word "stem" to refer to the portion shared in common at the start of all of the 'oblique' inflected forms of a noun or adjective. 'Oblique' in this context means that we ignore nominative singular forms.
Method 1: Take the comparative adjective's genitive singular form and remove -is from the end
The standard rule for finding this oblique stem is to start with the genitive singular form, and remove what Latin teachers regard as the "ending": -ae, -ī, -is, -ūs, or -ēī/-eī, depending on the declension. Actually, you could also find it by removing endings from another oblique form, but using the genitive singular is conventional (most dictionaries don't supply any other oblique form) and convenient because the genitive singular has less variation in endings than other oblique forms.
(How words are divided into stems, suffixes and endings may have different answers depending on if you're a Latin teacher or a historical or theoretical linguist).
This applies equally to nouns, positive adjectives, and comparative adjectives: in all cases, the oblique stem is equivalent to the genitive singular with -ae, -ī, -is, -ūs, or -ēī/-eī removed:
- amīcus (masculine noun) has the genitive singular amīcī and the stem amīc-
- pulcher (masculine positive adjective) has the genitive singular pulchrī and the stem pulchr-
- pulchrior (comparative adjective) has the genitive singular pulchriōris and the stem pulchriōr-
So if you have the genitive singular, you can find the oblique stem per the above process.
Method 2: Take the positive adjective's feminine nominative singular form, remove -a or -is from the end, then add -iōr- OR Take the positive adjective's genitive singular form, remove -is from the end, then add -iōr-
For adjectives other than third declension adjectives "of one ending", dictionaries typically supply two or three nominative singular forms.
In this context, you can find the oblique stem by removing -a or -is from the feminine nominative singular form. As I discussed in response to your previous question, the feminine nominative singular does not in general have a special relationship with the oblique stem of a word; the only reason you use it in this case is because dictionaries conventionally list it, and for adjectives of these types it has a predictable relationship to the stem. You could find the stem equally well by removing the ending from the positive adjective's genitive singular form, if you knew what it was (which is why dictionaries list the genitive singular for adjectives like audāx, audācis).
Once you have the oblique stem of the positive adjective, you add -iōr- to it to form the oblique stem of a regular comparative adjective. Thus, pulchr- + -iōr-, giving us pulchriōr- as the oblique stem of the comparative. Adding -is to this gives us pulchriōris, the genitive singular form of the comparative. The masculine/feminine nominative singular of the comparative differs in vowel length: pulchrior, and the neuter nominative/accusative singular is pulchrius. Latin teachers normally just treat the nominative singular forms of third-declension words as something for learners to memorize in addition to the oblique stem, although nominative singular forms do follow largely predictable patterns.
Regular comparative adjectives always have an oblique stem ending in -iōr-, a masculine/feminine nominative singular form ending in -ior, and a neuter nominative/accusative singular form ending in -ius.