Nominalization is making another part of speech--verbs, adjectives, phrases, abstract nouns, etc.--noun-like. Nominalization is mainly done with the help of 形式名詞 (nominal/dummy nouns).
The nominalizers の and こと are both used to nominalize phrases to make them noun-like to an extent. At the most basic understanding, the main difference between the two is that the former is more subjective and the latter is more objective. This small yet important difference places a major role in how they are chosen and how they fit with other expressions.
An objective perspective is one that is not influenced by personal emotions whereas a subject perspective is one that does involve emotion. こと literally means "matter/circumstance," and so it is used in grammatical situations where one needs to nominalize verbal/adjectival expressions and concretely talk about them as entities. For instance, if you want to talk about "new developments" or "dancing," こと would appear.
However, a more subjective circumstance will most likely call for の. It is a dummy noun, meaning it doesn't have all the freedoms of a true noun. That's why we see it in grammar patterns like のだ. When there is no need to portray an objective stance, の will also be the appropriate choice.
Orthography Note: こと is frequently spelled as 事.
Examples of こと & の
1. 見ることは信ずることである。
Seeing is believing.
Grammar Note: Whereas の is a dummy noun, こと is a true noun. Although Ex. 1 is a rather subjective thing to say, there is a sense of certainty that can be felt with the use of こと. However, at a more basic understanding of grammar,the use of こと is also necessary to set up the grammatical parallelism and comparison being made between "seeing" and "believing." These entities need to be expressed with true nouns, which is something that only こと can make possible.
2. お二人が会うのは初めてですか。
Is this the first time you two have met?
3. カナダが寒いことに気づいた。(Objective)
I just noticed that Canada is cold.
4. カナダがペンギンも生きれるほど寒いのに気づいたばっかりだわ。(Feminine)
I just realized that Canada is cold enough for penguins to even live.
Objectivity/subjectivity, although often a part of the equation, may not be the most important thing at work. In the following sentences, の just acts as a dummy noun for something else, but こと is more concrete, referring specifically to a situation. However, one can say that this is related to subjectivity being related to abstractness and objectivity being related to concreteness.
5. どんなのを聞きましたか。
What sort of thing did you listen to?
6. どんなことを聞きましたか。
What sort of thing did you hear/ask?
In the first sentence の replaces some noun such as 曲. In the second, こと refers to a situation (状態). The response could be something like the following.
7. 彼が京都に行った｛と・か｝聞きました。
I heard/asked that/whether he went to Kyoto.
Noun + のこと
At a basic understanding, there are two different yet intertwined functions of こと. The first is to focus on a certain action or state as the object of attention. The other is to expand the scope of something to encompass the situation surrounding it. In this latter sense, it abstracts. At face value, this seems like the opposite of focusing. However, this isn't really the case.
When こと attaches itself to verbs and adjectives, which in both cases could involve an entire sentence, こと packs up these expressions into a noun phrase, making it refer to the action/state at hand. This is the focusing aspect. When it follows a noun, however, it's following something that is already concrete to some extent. By using こと, which literally means "matter/circumstance," you're no longer literally talking about the physical entity at hand. Rather, you're talking about its essence, which is truly the matter at hand.
8. あの事件のことをよく覚えています。
I remember that incident well.
Sentence Note: In this example, the speaker remembers a lot about the incident. If のこと were omitted, the speaker would still remember that the incident happened, but it wouldn't necessarily sound that he/she knows much about the incident.
9. ピザのことをピッツァーと言う人がいます。
There are some people who pronounce "piza" as "pittsā."
10. この文は現在のことを言っています。
This sentence is talking about the present.
11. 誰の事を指しているんですか。
Who are you referring to?
12. 私たちはまだまだこの大きな地球のことを理解していないのです。
We still do not understand this great planet of ours.
13. 自分のことをどのくらい知っていますか。
How much do you know about yourself?
14. 僕のことがすき？
Do you like me?
Sentence Note: In this example, the speaker is asking the listener not just that the listener likes "him" in the mere sense of physical attraction. The speaker is asking if that individual likes him at a personal level as well. In the case of 好きだ and 嫌いだ, the use of のこと also helps solve semantic ambiguity between two possible interpretations. If the sentence were just 僕が好き？, it would normally be interpreted as "do you like me?" but it could also mean "Do I like...?" depending on the context. The use of のこと, thus, helps bring clarity to what is the object at hand.
More Examples
14. 彼が有名な音楽家だということを知りませんでした。
I didn't know that he is a famous musician.
15. あたし、そんなことはいわんかったわ。(Feminine; dialectical)
I didn't say anything like that!
16. もう一つ君に尋ねたいことがある。 (Male)
There's another thing I'd like to ask you about.
Speech Note: To a teacher say something more respectful like 先生、もう一つ伺いたいことがあるんですけれども（よろしいですか）。
17. （あなたが）見たことを話してくださいませんか。
Could you tell me what you saw?
18. 恋人たちは一緒にサンバを踊るのをやめました。
The couple stopped dancing the samba together.
19. 毎日散歩するのは健康にとてもいいようです。
It seems that going for a walk every day is very good for your health.
20. 彼女が昨夜遅く帰ってきたことを知ってた。
I've known that she came home late last night.
21. 彼女のいうことを真に受けたな。
You took her at her word, didn't you?
22. 何か心配なことがあるんですか。
Is anything bothering you?
23. 新鮮な息を吸うことは素晴らしい。
Breathing fresh air is wonderful.
24. これからのことを考えるのは賢いですね。
It sure is wise to think about the future?
25. 容疑者がその部屋から慌てて出てくるのを見ましたよ。
I saw the suspect come out flustered from the room.
26. 宿題をしないで授業に来るのはよくないです。
It's not good to come to class without having done our homework.
27. 生まれたのも育ったのもニューヨークです。
I was born and raised in New York.
Usage Note: It may be the case that の is used in place of a thing, person, or place. In this case の refers to the city that the speaker was raised in.
28. 彼女の電話番号を調べるのに時間がかかった。
It took a lot of time to find her phone number.
29. 歌うことは諦めていただけに偶然（に）初舞台を踏めたことはとても嬉しかったです。
Since I had given up singing, being able to debut by chance was very delightful.
30. 教育を受けるのは重要です。
Receiving an education is important.
31. 警察が今ここにあることは疑えない。
You can't doubt that there are police here now.
33. 日本が経済大国になれたのは、何と言ってもアメリカのおかげではないと思います。
No matter what they say, I don't think that Japan was able to become an economic power thanks to America.
34. 単純労働でお金を稼ぐのは大変だ。
It is difficult to earn money by simple labor.
35. 生まれたのは中国だが、国籍はインドネシアだ。
I was born in China, but my nationality is Indonesian.
36. 明らかに情報をもう一度目を通すのは当然ですよ。
It's evident that we clearly look over the information once more.
Phrase Note: 目を通す ＝ To look/scan over.
お二人が会うのは、初めてですか。
Is this the first time that you two have met?
Honorifics Note: お- makes the sentence more polite to the addresses.
お二人が会うのは、初めてですか。
Is this the first time that you two have met?
Honorifics Note: お- makes the sentence more polite to the addresses.
もの nominalizes something to show that something is undoubtedly true.
37. 油は水に浮くものだ。
Oil floats on water.
38. 子犬になりたいものですわ！(Feminine)
I want to become a puppy!
39. よく金曜日に海で泳いだものだね。
I used to swim in the sea on Fridays, you know.
Phrase Note: よく…たものだ ＝ Used to.
Contraction Note: もの may be seen colloquially as もん.
Origin Note: もの comes from the noun 物.
もの・物・者
もの can be anything. This もの can be in particle constructions like above. 物 is a tangible and perhaps living thing. It can even be a spiritual force. It's in many set expressions. It can even be used as a prefix. 者 refers to a person humbly or in a condescending manner.
40. 物の怪にとりつかれる。
To be possessed by an evil spirit.
41. 物も言いようで角が立つ。
People may be offended by the way you speak.
42. 物の数分もしないうちに
In no more than a few minutes.
43. 物言えば唇寒し。（Proverb)
Least said, soonest mended.
44. 早い者勝ち。
First come, first served.