Look at older forms.
(See the end of this post for a tl;dr.)
For example, consider the third-declension noun lār, laris ("home spirit"). In Classical Latin this seems to be a standard R-stem noun: lār, laris, larī, larem, lare...
But in some very archaic Latin (such as the Carmen Arvale), the nominative plural is given as lases. This could mean that it used to be an S-stem lās, lasis instead.
How does that make sense? There are a set of standard sound changes which happened between the Old Latin of Plautus and Cato, and the Classical Latin of Cicero and Vergil.
- S became R in between vowels
- Compare flōris (formerly *flōsis) against flōs
- (More precisely, S became a Z sound between vowels. Later on, the Z sound became something like the American R; even later, that turned into the trilled Italian R.)
- VO usually became VE
- Compare vester against vōs
- DV became B
- Hence duellum (> "duel") became bellum, and duis (from duo) became bis
- Duo was used commonly enough to escape this change, just like it preserved the dual endings which otherwise died out.
- OS and OM at the end of a word became US and UM
- Compare tempus (earlier *tempos) with temporis (earlier *temposis)
- Or compare the Latin second-declension endings with the Greek ones
- And many others...
As you can see, following these backward is not a trivial process. (Though it is very very interesting.)
This is almost never necessary.
Latin regularized forms much more than Greek did. In Attic Greek especially, inflections often don't make sense unless you know the underlying forms. But in Latin, these irregularities were smoothed out over time: lār and honor became normal R-stem nouns; flōs and tempus are normal R-stems except for the nominative singular.
So if you know the nominative singular, which is sometimes unusual, and the genitive singular, which never is (because the ending starts with a vowel), you know everything you need to decline the noun properly.