The te-form of verbs is one of the more difficult parts of Japanese because it really is a small set of “facts” that you have to learn.
Most of what gets presented as the random “gotta-learn-em-all” facts of Japanese grammar actually aren’t that at all. They are part of a logical system that the textbooks never teach and I have explained the real secrets in my book Unlocking Japanese and in various articles and video-lessons.
However, the te-form of verbs is one exception in that there really are six different forms depending on how the verb ends, which you just have to know.
Mendokusai (Japanese for “pain in the petunia”), ne?
Fortunately it can be made a lot easier.
In this video I give a simple mind-map with mnemonics that will allow you to dominate the te-form in a very short time. The video is under 8 minutes and you may want to watch it a couple of times. But you should have the te-form of verbs conquered for life in under an hour!
Notes (and advice):
There are just three notable exceptions to the system presented here. They are Japan’s famous two irregular verbs kuru and suru, plus iku, “go”. Iku, instead of becoming the slightly awkward-sounding iite becomes itte. They work like this:
する （suru）→ して (shite)
来る （くる kuru） → 来て （きて kite）
行く （いく iku）→ 行って （いって itte）
Even though I mention these for completeness, I don’t recommend “learning” them now unless it feels easy.
My advice is, if these three feel confusing, just ignore them for now. Don’t let the whole system feel over-complex for the sake of these three. Consolidate the overall system in your mind. You will easily pick up the few exceptions over time.
A lot of people stay shaky on the te-form of verbs for a long time (especially recognizing it on the fly). With this system you can master the whole structure in a very short time.