Here's how I was taught verb conjugation.

First, we learnt verbs in the -masu form. Nomimasu, tabemasu and so on.

Then we learnt this song (to the tune of Clementine)

chi ri i tte mi ni bi nde kiite giite

It's a quick mneumonic to help you go from the polite verb to the "te-form" ending. I hummed it in my head while working out the conjugation before it became natural and "obvious".