The process of forming new words from old ones is called derivation.
In Latin you can derive adjectives from nouns, verbs, or other adjectives.
Here are some quick examples to illustrate that all directions are possible:
||navis > navicula
||canere > cantor
||audax > audacia
||laus > laudare
||edere > esurire
||novus > novare
||aurum > aureus
||audere > audax
||fessus > fessulus
Allen and Greenough treat deriving adjectives quite thoroughly.
(And not only adjectives, but other things are on other pages.)
When deriving adjectives from nouns, there are a couple of basic things you can do:
- (§243) Diminutives to denote smaller size, like my example navis > navicula.
- (§244) Patronymics to denote offspring, like Atlas > Atlantiades.
- (§245) Adjectives for being full of something, like nix > nivosus.
- (§246) Adjectives for describing what someone or something is equipped with, like barba > barbatus.
- (§247) Adjectives for materials or general relations, like nix > niveus.
- (§248) Adjectives describing a topic, like natura > naturalis.
The grammar I linked to lists a few more classes, but they fall in these general categories.
Every single one of these has a variety of different endings.
Some words require specific kinds of endings, and sometimes the different endings have differences in meaning.
If you want to derive an adjective from a noun, you have to know what the adjective should mean in relation to the noun.
Then you have to choose a suffix, bearing in mind that there are compatibility restrictions (see e.g. this question on -ulus/-olus).
In many cases there is already a fixed adjective, so you should follow the convention.
Sometimes there isn't, and then you have some freedom in derivation.
In such cases it is best to follow the analogy of similar words.
Derivation is so productive in Latin that deriving new words is certainly admissible but should be exercised with some moderation.