Japanese Revelations {(Verb 1) Without Doing (Verb 2)}

おはよう・こんにちは・こんばんは、みんなさん！
No matter what time it is where you are right now, I still say hello again!

So. This time, we're talking about how to say that someone did V1 without doing V2. Be careful, though - in Japanese, the order of the verbs is reversed. It would be more literally translated as, "Without doing V2, so-and-so did V1." A little more awkward, but it's simple enough! ^^
Making these types of sentences is easy enough, as well. For the verb you didn't do (we'll call this verb V2), just make it the plain, negative form. As in, the form that ends with ～ない. Then, add で after V2, and finally, stick the verb you did in spite of not doing V2 (which we'll call, V1) onto the end of the sentence. Also, V1 can be any tense and form, but V2 always ends with ～ない. Always.
Here's a helpful (in my humble opinion) formula (V1 and V2 are the same as they were for the last paragraph):
V2ないでV1.
That's all there is to it. Of course, if you want the sentence to be past tense, you're gonna have to change that yourself. Also, you can still add on things like a direct object, the indirect object, the location, etc. for either or both verbs.
Right. So, example sentences:
朝ごはんを食べないで、学校に行きました。
I went to school without eating breakfast. (Lit. Without eating breakfast, went to school.)

宿題をしないで、寝ます。
I went to bed without doing homework. (Lit. Without doing homework, go to bed.)

家族に話さないで、部屋へ行きました。
I went to my room without talking to my parents. (Lit. Without talking to parents, went to room.)

Of course, all these sentences (or any sentence you can come up with!) can be informal, negative, informal negative, heck, even volitional, causative, or passive! Here are some examples with those last three options in the order they're mentioned:

ボールペンで描かないで、バレンタインのカードを作りましょう。
Let's make Valentine's cards without using pens. (Lit. Without using pens, let's make Valentine's cards.)

待たないで、宿題をさせる。
We were made to do our homework right away. (Lit. Without waiting, we were made to do our homework.)

水滴もない惜しまないで、全部の水を飲まれる。
All the water was swallowed without sparing a drop. (Lit. Without sparing even a drop of water, all the water was swallowed.)

Causative-Passive! (See sentence and description below.)

晩ごはんを食べないで、部屋へ行かせられる。
I was sent to my room without eating dinner. (Lit. Without eating dinner, was made to go to room.)
Note: this uses what's called 'causative-passive' form, meaning someone was made to do something, and they quite frankly had no choice in the matter.
Also, please realize that using the causative form (to let someone do something) to ask to go to the bathroom or something like that sounds like a prisoner, even when translated to English - it would sound like this:
トイレいかせてくれますか？
Or, in English:
Can you let me go to the bathroom?
No. Just, no. (This little tidbit courtesy of Tae Kim's Guide to Japanese Grammar, in particular, this page.)

Well, that's it. If it's hard to remember, think of it like this: で is used when talking about 'by way of ____', right? Such as by bus, by car, etc? This is like saying 'by way of not V2, so-and-so did V1'. Maybe it's not the best explanation, but then again, I'm not a teacher, and it's the best I could come up with.

Enjoy and good luck!