The て-form (te-form) in Japanese is used in three different occasions: when making requests, asking and receiving permission, and describing two activities in a sentence. We can differentiate between these three usages by the additional ending added.
The first usage for the て-form is for making requests. When we use the て-form in this way, the ending becomes ～てください (~tekudasai): this means we take the verb and conjugate it into the て-form, then add ください (kudasai). ください means “please" in English, so these て-form requests are a polite way to say “please do...for me." Let's look at some examples:
この ページ を よんでください。(kono peeji wo yondekudasai)
Please read this page (for me).
みせ に いってください。(mise ni ittekudasai)
Please go to the store (for me).
Notice in the first example the verb is よんでください: the て can change to で, depending on what the て-form is.
The て-form can also be used to ask permission. The specific ending is ～てもいいです (~temoiidesu). Let's look at an example:
コンピューター を みてもいいですか。(konpyuutaa wo mitemoiidesu ka)
May I see the computer?
If we want to give the asking person permission, we can use the ～てもいいです ending. For example:
Yes, you may.
However, if we do not want to give permission, we use another ending: ～てはいけません (~tehaikemasen). For example:
いいえ、コンピューター を みてはいけません。(iie, conpyuutaa wo mitehaikemasen)
No, you may not see the computer.
Two Events or Activities
Another way the て-form is used is to describe two events in the same sentence, which requires two different verbs. The formula for this type of sentence is:
The verb that is conjugated in the て-form equals “and." The second verb is conjugated in either present tense or past tense, depending on the time frame of the sentence. Here's an example how the Vて、Vます formula is used:
きょう は、ろくじ に かえって、たべました。(kyou wa, rokuji ni kaette, tabemashita)
Today, I came back at six o'clock and ate.
When using this type of て-form sentence, the verb that is conjugated in the て-form is the event that comes first. This applies to sentences about the future: the first proposed activity would be conjugated in the て-form, then the second form in present tense.
Banno, E., Ohno, Y., Sakane, Y. and Shinagawa, C. An Integrated Course in Elementary Japanese. The Japan Times, 1999