Below are simple explanations and examples just for a quick review, provided for your reference. You should go back to your textbooks for a complete review. The lesson numbers correspond with lessons in the Genki I textbook.
は: Topic particle. It marks the topic of the sentence. The meaning is close to 'As for~' or 'Talking about~'.
メアリーさんは にねんせいです。As for Mary, (she) is a 2nd-year student.
このほんは たかいです。Talking about this book, (it) is expensive.
Sentential subjects often become the topic of the sentence, but はcan be used after sentential objects or time expressions depending on what has been talked about. However, the use of はis restricted. Do not overuse は.
か: Question particle. It attaches at the end of a sentence to make a question (with rising intonation).
メアリーさんは にねんせいですか。 Is Mary a 2nd-year student?
このほんは たかいですか。Is this book expensive?
よ: Sentence-final particle. Providing the information unknown to the listener.
メアリーさんは アメリカ人ですよ。(In case you don't know) Mary is American.
このすしは おいしいですよ。(I'm telling you) this sushi is tasty.
ね: Sentence-final particle. Used to ask for confirmation or agreement.
メアリーさんは アメリカ人ですね。Mary is American, right?
このすしは おいしいですね。This sushi is tasty, don't you think?
の: ~'s, of ~. Be careful with the word order. Japanese particles attach at the end of the word or phrase.
メアリーさんの ほん Mary's book
だいがくの としょかん the library of the university (= the university library)
Verb の (Lesson 8)
Here, の is used as a nominalizer; it attaches to a verb and turns it into a noun phrase, so that it can be used as the subject/object in a sentence.
メアリーさんは テニスを するのが すきです。Mary likes playing tennis.
Adjective/noun+の (Lesson 11)
Following an adjective, の is used like 'one' in English, when it is clear from the context what it refers to.
くろいくつ black shoes ⇒ くろいの black ones
When the second noun in「AのB」 is clear from the context, you can omit B. This is like -'s in English.
メアリーさんのほん Mary's book ⇒ メアリーさんの Mary's
で:
1) Place of action (Lesson 3): in, at. Indicates the location where the action takes place.
（わたしは）レストランで ひるごはんを たべました。I ate lunch at a restaurant.
スーさんは かんこくで にほんごをべんきょうしました。Sue studied Japanese in Korea.
2) Means of transportation, instrument (Lesson 10): by, with
メアリーさんは バスで だいがくに きます。Mary comes to the university by bus.
（わたしは）はしで すしを たべました。I ate sushi with chopsticks.
に:
1) Time expressions (Lesson 3): Used after time expressions such as days of the week, time, months, years.
にちようびに べんきょうしました。I studied on Sunday.
五月(ごがつ)に 日本(にほん)に いきます。 I will go to Japan in May.
Some time expressions do not need に, such as あした、きょう、らいしゅう、ことし、まいにち、いつ, etc.
（わたしは）きょう＿ だいがくに いきます。I will go to the University today.
（わたしは）せんしゅう＿ にほんごを べんきょうしました。I studied Japanese last week.
2) Direction (Lesson 3): to, toward
としょかんに いきます。I will go to the library.
クラスに いきました。I went to the class.
Certain verbs take に, not を.
バスに のりました。I took a bus (=I got on the bus).
まいにち おふろに はいります。I take a bath every day (=I enter into the bath every day)
きのう ともだちに あいました。I met a friend yesterday.
3) Location (Lesson 4): Location where something/someone exists.
としょかんに 本(ほん)が あります。There are books in the library.
うちに ねこが います。There is a cat in my place.
Location words with certain verbs take に instead of で (Lesson 7). It is easier to memorize them in this category than individually.
（わたしは）おおさかのかいしゃに つとめています。I works for a company in Osaka.
メアリーさんは きょうとに すんでいます。Mary lives in Kyoto.
つとめるand すむare not actions. Rather, they are states and so they cannot be used with で.
4) Place に Verb(purpose) に いきます/きます/かえります (Lesson 7). When you go/come/return somewhere in order to do something, use this structure.
としょかんに 本をかりに 行きました。I went to the library to borrow a book.
まいにち このきっさてんに おちゃを のみに きます。Every day I come to this coffee shop to drink tea.
へ: Destination. Similar to (2) in に above. Used with the change of location verbs いきます, きます, orかえります.
（わたしは） うちへ かえります。I will return home.
メアリーさんは とうきょうへ いきます。Mary goes/will go to Tokyo.
を: Direct object particle. No equivalent in English. It marks the direct object of the verb.
（わたしは） すしを たべます。I eat sushi.
メアリーさんは しんぶんを よみます。Mary reads newspaper.
も: Similar to English too or also. Where the particle attaches is tricky. Two entities share the same attribute. The second entity should be followed by も. It replaces は、が、を.
メアリーさんは にねんせいです。わたしも にねんせいです。
Mary is a 2nd-year student. I am 2nd-year student, too.
（わたしは）コーヒーを のみました。おちゃも のみました。
I drank coffee. I drank tea, too.
It attaches after に、へ、で (Lesson 4).
メアリーさんは どようびに でかけました。にちようびにも でかけました。
Mary went out on Saturday. (She) went out on Sunday, too.
（わたしは）うちで べんきょうします。としょかんでも べんきょうします。
I study at home. I study at the library, too.
が: Subject particle. No equivalent in English. It marks the subject of the sentence. While many Japanese sentences tend to take the 'Topic+Comment' structure with ～は, the subject particle is used in specific structures/functions as follows.
1) Existence of something/someone (Lesson 4) 「placeにthing/personがあります／います」
へやに テレビが ありません。There isn't a TV in the room.
としょかんに がくせいが います。There is a student in the library.
2) likes and dislikes (Lesson 5)「personはthingがすきです／きらいです」
わたしは すしが すきです。I like sushi.
メアリーさんは れきしが きらいです。Mary dislikes history.
3) Physical attributes (Lesson 7) 「personはbody partがadjective」
メアリーさんは かみが ながいです。Mary has long hair. (As for Mary, her hair is long)
たけしさんは せが たかいです。Takeshi is tall (As for Takeshi, his height is high).
4) With question words in the subject position (Lesson 8): When a question word appears in the subject position, you must use が (you cannot use は). The answers to such questions should also use が in the subject position.
だれが パーティーに きますか。Who comes to the party?
スーさんが パーティーに きます。Sue comes to the party.
どのほんが おもしろいですか。Which book is interesting?
5) With emphasis (Lesson 8): In English you use intonation to emphasize one of the entities in the sentence. In Japanese, the subject particle has this function, emphasizing the subject.
メアリーさんが すしを つくりました。MARY made sushi.
わたしが たけしさんと はなします。*I* will talk with Takeshi.
*The distinction between は andが is very complicated. Since this is practice for introductory level learners, you just need to know the structures that require the subject particleが.
と:
1) Connect two or more than two (pro)nouns. (noun) and (noun). Cannot connect verbs or adjectives.
みずとおちゃ water and tea
これとそれ this and that
2) together with~
スーさんは メアリーさんと でかけました。Sue went out with Mary
や (Lesson 11):
Similar to と. Implies that there are others that are not mentioned.
とんかつや すし tonkatsu, sushi, and others
とんかつと すし tonkatsu and sushi (and nothing else)