For all that I'm not totally sold on this article's idea of "stems" and "suffixes", I think it does a good job of avoiding this pitfall and correctly explaining the groups.
An important aspect of vocabulary that informs you about verbs is knowing the nominal: the noun-like stem. Like when you consider 帰る, you know from your vocabulary that there is no noun-like word "kae" that is just written 帰. You know that "homecoming" is not "kae" but "kaeri", 帰り.
So from that alone you know instinctively which way it conjugates: らない、れない、りたい、った、って、ろう、。。。
And a big source of learning the stem is ... japanese polite speech with -masu.
This is how children absorb what the stems are: hearing all the verbs in -masu form.
For instance, I think that every single verb that ends in "-rimasu" in the polite form (other than just arimasu?) is a godan -ru word. Drop the masu and you have a -ri stem, which implies the word is -ru, and conjugates godan: -ranai, -renai, -ritai, -rō, -tta, -tte, ...
Not quite: https://jisho.org/search/%23words%20%23v1%20%3F*%E3%82%8A%E3...
I don't have a problem actually conjugating and don't have any tricks for it.
It comes with vocabulary. Once you have a vocabulary that contains enough verbs to hit all the cases, the rest just land in one of the cases by example.
If you know 泳ぐ (oyogu) very well, then even though you don't use 仰ぐ (aogu) very much, you just conjugate it intuitively like oyogu.
When you're speaking, there isn't enough time to go through a roster of rules.