The reason you sometimes find a 「る」 after a て-form of a verb is here:
When you add 「～いる」 (used as a something progressive or continuous tense) at the end of a て-form of a verb, you get 「～ている/～でいる」. But, colloquially, the 「い」 is dropped, leaving behind as 「～てる/～でる」.
Either suffix is able to be conjugated as a ru-verb because the previous vowel was either /e/ or /i/, so you get (te-form for this) 「～ていて/～でいて」 or 「～てて/～でて」.
An example here would be with 「死ぬ」. 「死んでいる」 and 「死んでる」.

I know all the te-form, ta-form, plain-form, etc. But in a couple of instances I’ve seen an extra ‘ru’ added to the end of a te-form verb.

An example is: ‘mite’ being turned into ‘miteru’.

I’ve been curious as to what that changes the meaning to, and why it is used. I’ve studied a couple of gramatical structures such as adding a ‘ra’ to the end for ‘if you (verb)’, and how to say things such as ‘I intend to (verb)’, etc. However, this wasn’t mentioned among all the others.

As an extra! I know an easy way to remember te-form! It can be sung~ Haha

I Chi Ri – Tte
Mi Ni Bi – Nde
Ki – Ite
Gi – Ide
(This line was something along the lines of ‘Shi Shi – Te’, though I think I misheard and it is actually something like ‘E Shi – Te’ If it is ‘Shi Shi – Te’ then I assume the second ‘shi’ stands for single character verbs)
All the rest of the verbs, just drop the masu and add the te! ^_^

Well then! I’d appreciate it if you could answer my question! Thanks in advance!

Thanks for the kind words and good luck tomorrow.

ありがと!!!

Well, it is not so easy, because this is one place where Japanese differs from English and European languages. It is an Asian language, after all, and moreover, a Chinese-influenced language.

歩いて　ー　walk-ing

It is a form of a verb, but at the same time it is the form of a Japanese verb, not an English verb. It is “~ing” not in the sense of “is ~ing”, but in the sense of “~ing is good”, So, “walking” as in “walking is good for your health”, which would be the nominalized verb in English, rather than the continuous form.

“te”-form also indicates – grammatically speaking – that a verb is expected at the end of the sentence or sentential clause.

This is a good question, but nobody ever answers it, because they don’t approach it that way. They approach the meaning of specific use of the form, but not what the form suggests about a sentence.

The te-form of a verb is like a na-adjective, except that the na-adjective indicates a noun coming up, whereas the te-form indicates a noun is coming up. The -ku form of an adjective is the adverbial form of the adjective, it indicates an action done in a specifc manner. The te-form of a verb indicates that the two verbs are related to each other in an “~ish” kind of way. “aruite-iku” or “aruite-yuku” is “going a in a manner like walking”; Japanese is more “holistic”.

“aruite-iru” is used in a present continuous sense, but it means “(to) be walking”. That’s why it can be used as a “polite command”, just like it is used in English. The “iru” is implied when it is used as a command.

Japanese is a far more regular language, having been isolated for so long, but it is hard if you don’t understand its regularities.

anyway,

Have fun!

またね！（僕は今勉強すればスパヌ語があるかな。。。）ために。。。

歩く　ー　to walk
歩いて　ー　??

Thank you!
Marsha.

I think basically the information that DumbOtaku is presenting here is very similar to what there is on the link provided. Basically however instead of putting work into learning the learning the different ways of forming the te form of the verb, the link you provided is advocating first learning the informal past negative of a verb, and then after that the te form is quite simple. However, the work of memorization and relying upon a table is still there, just that it has been shifted to a different form of the verb. In the long run one way does not seem easier or harder than the other.

Thanks again for taking the time to comment.

Hope I helped. I'm not a native speaker by any stretch of the imagination but those pages helped me a lot in understanding Japanese verbs.

Good luck with learning Japanese!

P.S. Sorry about having to split the message up into parts. Apparently there's a length restriction.