Particle classification is very important to keep in mind as you learn more about particles. The particle て discussed in this lesson is a final particle and mustn't be confused with the conjunctive one. Although the conjunctive て may be at the end of a sentence in the instance that the remaining part of a sentence is not said, overall context should always help you differentiate between the two.
The main purpose of the final particle て is to make a light command. This is the contraction of ～てください, the polite command. Likewise, the negative of this is ～ないで（ください）, making the absence of ください a contracted form of the pattern. Thus, its absence for both the affirmative and negative makes it go from polite to plain speech. A more polite form of both can be made by changing ください to くださいませんか.
1. ちょっと待って。（Casual)
Hold on.
2. 払い戻ししてください。
Please refund this.
3. 助けて！
Help!
4. 教科書を｛閉じて・しまって｝テストを受けてください。
Please do your test by closing your textbooks.
5. やめて！
Quit it!
6. これを見て。
Look at this.
7. タクシーを呼んでください。
Please call a taxi (for me).
8. はやく急いで！
Hurry quickly!
9. もっとゆっくりと話してください。
Please speak more slowly.
10. 速くしてよ！
(Do it) faster!
11. まっすぐ行ってください。
Please go straight.
12. 座布団を敷いてください。
Please sit on a cushion.
Culture Note: 座布団 are floor cushions used instead of chairs in traditional Japanese rooms.
Contraction Note: ～てて is the contraction of ～ていて. ～ている means "-ing". ～ていて creates a command similar to "be...-ing!".
In women's speech, ～(っ)てよ asserts opinion. However, this phrase has essentially disappeared in the younger generations and is most likely to be used by older women or seen in literature dating back a few decades ago. It is replaced by things such as ～てるよ.
13. あたくし、ちっとも酔ってなんかいなくてよ。
I'm not even the least bit drunk.
From 永すぎた春 by 三島由紀夫.
Particle Note: なんか is essentially a filler word here.
14. かまわなくってよ。～て, with a high intonation, can make a question. These two usages, though, are hackneyed yet refined. This, too, would be replaced with something like ～てる？.
15. あなた、私のいうことが分かって？It is to note that ～てよ is used by everyone to make a command. The sound of your voice is what matters.
～て may also follow things like だ・じゃ to tell someone to do something or give some sort of instruction/warning. This, though, is uncommon.
16. 大変なことじゃて。（Old person; dialectical)
That's a horrible thing!