A conjunction is a word that is used to combine two elements into a more complex phrase or sentence.
A conjunctive conjugation combines two similar elements into a more complex phrase.
This is essentially equivalent to the English or when it doesn't come at the end of a sentence. Essentially, write the sentence out with the last noun only as you normally would. Then, put the other choices in front of the last choice and place か after each of them.
コーヒーか おちゃか みずが ほしいか。
Would you like coffee, tea, or water?
This is similar to the English and when it follows a noun. Sometimes, the other part of the combination is assumed, particularly if it is the speaker. When you use と as a conjunction, it is assumed that you are listing out all of the elements of the combination. If you are not listing out all of the elements, use や.
ともだちの むらかみさんと いっしょに とうきょうに いきます。
My friend, Mr. Murakami, and I are going to Tokyo together.
ほんと かみと えんぴつを かいました。
I bought a book, some paper, and a pencil.
This is also similar to the English and, but implies that elements of the combination are missing. Essentially, this is like listing out a group of items or people and tagging it with etc. or et al.. Sentences are formed much the same way as they would with と.
カバンの なかに ほんや かみや しゅくだいが あります。
There's a book, some paper, homework, and other stuff in my bag.
Adjectives are combined by using the "conjunctive" conjugation. For ～い-type adjectives, replace the ～い ending with ～くて; for な-type adjectives, place a で after the adjective.
ひろくて しずかで すずしい いえを さがします。
I'm looking for a spacious, quiet, cool house.
Verbs are also combined by using the "conjunctive" conjugation, which is typically referred to as the ～て conjugation.
たべて のんで よろこんで ください。
Eat, drink, and be merry.
Phrases can also be combined. Most of the time, the individual phrases can form entire sentences, but the conjunction indicates the relationship between one sentence and another.
Though the example above used only verbs, the conjunctive can be used to combine predicate phrases that share a common subject. Much like と, this implies that the list given includes all elements of the combination.
けさ ねぼう して はを みがいて あさごはんを たべて しごとに いきました。
This morning, I overslept, brushed my teeth, ate breakfast, and went to work.
Sometimes referred to as the ～たり form, this is to the conjunctive form for verbs what や is to と for nouns. It enumerates a list non-exhaustively, letting the audience fill in the rest of the list.
きのう かのじょと いっしょに えいがを みましたり かいもの したり きっさてんで たべたり しました。
Yesterday, my girlfriend and I watched a movie, did some shopping, ate at a coffee shop, and so forth.
Not only used for nouns, か can be extended to combine phrases together to provide a list of choices.
ピアノを ひくか ビデオゲームを するか そうじ すれば いいか。
Should I play the piano, play a video game, or do the cleaning?
The particle が can be used to introduce a contrastive statement.
パーティーに いきたかったが くるまは うごけませんでした。
I wanted to go to the party, but I couldn't start the car (lit. the car couldn't move).
The conjunctions でも and けれど can also be used to introduce a contrastive statement (much like "but" in English). けれど also appears as けれども (more polite) and けど (more informal). Unlike が, でも and けれど can sometimes be found at the beginning of a sentence.
きょねん とうきょうに いった けれど にほんごが よく まなびませんでした。
I went to Tokyo last year, but I didn't learn much Japanese.
The conjunction から trails an explanatory statement, usually introducing a statement of something affected by the previous statement. It can usually be translated as "because". It will sometimes appear as だから at the beginning of a sentence if the explanation was given in a prior statement, especially if a different speaker presented the explanation.
きょうは やすみから ねぼう しました。
I have today off, so I slept in. (or Because I have the day off, I slept in.)