Talking about the examples, which you've showed, i would explain them this way: "I got it" ,means "I understand" or "I have something" ,
"I got that" means only "i understand" , rarely it means "i understand"
"I got one" means only "I have something"

As you see it's pretty comfortable to use "I got it", 'cause in most situations is fits well. =))

Thank you, Nami.
I think that I could get your exposition.
So I can say, "I got IT!"

I'll be counting on you.

"I got it." Can mean a few different things depending on the context it's used it. It can mean "分かりました" or that you're agreeing to do something that's requested of you. For example, the phone is ringing. You can say "I got it!" to mean that you're going to answer the phone. It can also mean you received or purchased something. For example, "Did you get the e-mail I sent you?". You can answer "Yes, I got it."

"I got that" is similar to "I got it", except it means you're understood one specific thing. The usage is a little more tricky with this one and I'm having trouble coming up with a clear example and sometimes precedes something else. "Did you know we're all getting vacation next month?" "Yes, I got that from the e-mail the president sent." Or, "Did you hear Shonen Knife came out with a new CD?", "Yeah, I got that." (although "I got it" would work perfectly fine here).

"I got one" is different than the other two. It simply means you received/purchased one specific thing. For example, "The new I-pod came out this week." You could reply. "I got one." or "The company president is giving Pocky to all the employees today. Did you get one?" "Yes I got one!"

Hope that helps. :)

Good morning (evening?), domokun1134さん.

I'm clear!?
Because you say "I'm having trouble coming up with a clear example", I think it is a sensitive point, isn't it?

I have another question.
Is ↓ right?

I picked up a pen, and I hold IT.
When my friend says that he lost his pen, I say, "I hold THAT".

"Do you know the Apple new product, iPad?"
I say, "I want ONE."

Am I correct?

For your second question:

If you picked up a pen, and you hold it. When your friend says he lost it you would say"I have it"

Do you know Apple's new product, iPad?
"I want one" or "I want it" -- Both of the phrases are correct.

Hello, MujicaDesu!
Nice to meet you.
Thank you for your comment.
So can I use "it" anytime?

I live in Kanagawa pref. near Kawasaki-city!
Where do you want to go when you come to Japan?
Akihabara? Shinjuku? or Disneyland?

I got it - 分かりました, なるほど

I got that - それは/が分かりました

I got one - これ/それ/あれがあります

にんきさん、こんにちは。
it, that, oneはそんなに使い分けに気を遣う必要はないんですか。
どれを使っても、言いたいことは通じるんですかね。

Could you teach me that I don't need to use these words as the situation demands?

Ok, I'll try to explain it in simple terms so that you'll understand better.

質問一：
Did you understand my explanation? （私の説明する事は分かりますか？）

答え：
a.) I got it - （”はい、分かった” 、”了解”）ーいい答えです

b.) I got that - （”はい、分かった”、”了解”）ーいい答えです

c.) I got one - （”一つがあります。。。”）－この答えは違います


問題二：
Do you have good memories last summer? 前の夏にいい思いがありますか？

答え：
a.) I got it - （”はい、分かった” 、”了解”）ーこの答えは違います

b.) I got that - （”はい、分かった”、”了解”）ーこの答えは違います

c.) I got one - （”はい、一つがあります。。。”）－いい答えです


質問三：
Did you understand these two problems? この二つ問題は分かりましたか？

答え：
a.) I got it - （”はい、分かった” 、”了解”）ーいい答えです。全部分かります。

b.) I got that but...- （”はい、分かったでも。。。”）ーいい答えですけど一つ問題しか分かりません。

c.) I got one - （”はい、一つがあります。。。”）－この場合にはこの答えがちょっとへんです。使いないほうがいい。

I hope I gave you a better explanation. If you still don't understand, just let me know.
はっきりで説明する頑張った。もし、まだ分からなかったらぜひ教えてくだあさい。

Thank you, にんきさん。
質問一： I got it!!!
質問二： I go it. c) I got one. Does the ONE mean as 1 of 1,2,3?
質問三： I got it.

「質問三」を読んで、”it”は全体を、”that”は"it"よりも具体的なものを指し示すと感じたのですが。
I think that "it" represents the whole thing, and "that" represents more specific than "it".

Katsuさん、

はいそうです。もう分かりますと思う、がんばって使ってくださいね。

にんきさん、ホント、お世話をおかけしました。<(_ _)>

"I'm clear!?
Because you say "I'm having trouble coming up with a clear example", I think it is a sensitive point, isn't it?"

Haha, no I wasn't calling you 'clear'. Let me explain. When one says "clear example" it doesn't mean they're calling you 'clear', which wouldn't make much sense anyway. When the word 'clear' is used in this way it means "easy to understand" or that the meaning isn't hidden. 'Clear' generally means something that you can see through, so a "clear example" is an example that you can "see through to get to the real meaning".

It can also be used to describe how well you can hear or see something. For example an eye doctor would hold out a chart for you to read to check your eyes. When he asks if you can read it you can reply "I can see it clearly", if you can see it perfectly.

I wish I could explain in Japanese because it would be easier for you to understand, but my Japanese isn't good enough yet. :(

Good morning, domokun1134さん！
Thank you for your advice, I don't know that I got how to use "it" or "that" or "one" clearly.
(Maybe I think I can use these ("it", "that", "one") correctly.)
But I'm many times clearer than before.

Your Japanese is not bat, I can get easily what you mean.
(Of course, also your explanation in English is easy to understand for me.
Sometimes I don't understand your advice because of my English skill...)

I have to study more. Could you kindly continue to correct my entry?