(1) Placed between two nouns, the particle と translates as 'and'.
Ex : 犬いぬと猫ねこがいる。There is a dog and a cat.

(2) と can also indicate that an action is performed with someone, in which case it is translated as "with".
Ex : 昨日きのう、先生せんせいと話はなした。Yesterday I talked with my teacher.

や is also used between two nouns, but it assumes an incomplete enumeration.
など・等など is often put after the last word of the enumeration (can be translated as "etc.").
Ex : お昼ひるは、おにぎりやサラダやバナナなどを食たべた。I had an onigiri, a salad, a banana, etc.

とか is a more familiar expression than や.
Ex : ドラマとか映画えいがとかアニメを見みる。I watch a series, a film, an anime, etc.

(1) の introduces a noun complement.
Ex : 田中たなかさんは、日本語にほんごの先生せんせいだ。Tanaka is a Japanese language teacher.

(2) の also means belonging.
Ex : これは、私わたしの車くるまだ。This is my car.

Notes on the use of の

- The name that is changed may be omitted depending on the context.
A：それは誰だれのかばん？Whose bag is it ?
B：まことくんの。This is (the bag is) Makoto's.

- の can replace and take the role of the name itself.
adjective + の　→ a thing + adjective 
Ex : 青あおいの (a blue thing) 

- If we put an adjective in な before の, we must add な between the adjective and の.
Ex : 私わたしが好すきなのは、ゲームだ。One thing I like is games.

- After a verb, の introduces a nominalization of the verb. Then you can use like any noun.
Ex : スーパーへ行いくのを忘わすれた。I forgot to go to the supermarket.

- Generally, 物もの is used instead of の when it is a physical object and こと for events.
Ex : 青あおいの　→　青あおい物もの
私わたしが好すきなのは、ゲームだ。　→　私わたしが好 きな物ものは、ゲームだ。
スーパーへ行いくのを忘わすれた。　→　スーパーへ行いくことを忘わすれた。

We use の to explain or ask for a reason, an explanation.

A: どうしたの。What is happening to you? (seeking for explanations)
B: 頭あたまが痛いたいの。I have a headache. (giving explanations)

A: 学校がっこうへ行いかないの？You don't go to school (How come you don't go to school?)
B: 今いまから行いくよ。I'm going there now.

Remarks on the use of the explanatory の

- Often used with どうして (why).
Ex : どうして食たべないの。Why don't you eat?

- If の is put in front of a noun, な must be added between the noun and の to distinguish it from the particle の which means belonging ("to" or "of").
Ex : 車くるまは、ジャックのだ。The car belongs to Jacques.
社長しゃちょうになるのは、ジャックなのだ。It is Jacques who becomes president of the company (with an explanatory tone).

- We also add な after adjectives in -な.
皆みんな山田やまださんが好すきだ。山田やまださんはとても親切しんせつなのだ。Everyone loves Yamada. Because he is very nice.

-「のだ」is used more in written language. In conversation, it is preferred「んだ」.
A: あれ、今日きょう仕事しごとはないの？
B: うん、休やすみなんだ。